diff --git a/ast/functions.go b/ast/functions.go
index 3245780bfb..e49aa17a9b 100644
--- a/ast/functions.go
+++ b/ast/functions.go
@@ -425,7 +425,7 @@ func (n *AggregateFuncExpr) Update() error {
 		return n.updateMaxMin(true)
 	case AggFuncMin:
 		return n.updateMaxMin(false)
-	case AggFuncSum:
+	case AggFuncSum, AggFuncAvg:
 		return n.updateSum()
 	case AggFuncGroupConcat:
 		return n.updateGroupConcat()
@@ -534,6 +534,7 @@ func (n *AggregateFuncExpr) updateSum() error {
 	if err != nil {
 		return errors.Trace(err)
 	}
+	ctx.Count++
 	return nil
 }
 
diff --git a/optimizer/evaluator/evaluator.go b/optimizer/evaluator/evaluator.go
index ea1a8b12e7..0d8821fb32 100644
--- a/optimizer/evaluator/evaluator.go
+++ b/optimizer/evaluator/evaluator.go
@@ -956,6 +956,8 @@ func parseDayInterval(value interface{}) (int64, error) {
 func (e *Evaluator) aggregateFunc(v *ast.AggregateFuncExpr) bool {
 	name := strings.ToLower(v.F)
 	switch name {
+	case ast.AggFuncAvg:
+		e.evalAggAvg(v)
 	case ast.AggFuncCount:
 		e.evalAggCount(v)
 	case ast.AggFuncFirstRow, ast.AggFuncMax, ast.AggFuncMin, ast.AggFuncSum, ast.AggFuncGroupConcat:
@@ -973,3 +975,14 @@ func (e *Evaluator) evalAggSetValue(v *ast.AggregateFuncExpr) {
 	ctx := v.GetContext()
 	v.SetValue(ctx.Value)
 }
+
+func (e *Evaluator) evalAggAvg(v *ast.AggregateFuncExpr) {
+	ctx := v.GetContext()
+	switch x := ctx.Value.(type) {
+	case float64:
+		ctx.Value = x / float64(ctx.Count)
+	case mysql.Decimal:
+		ctx.Value = x.Div(mysql.NewDecimalFromUint(uint64(ctx.Count), 0))
+	}
+	v.SetValue(ctx.Value)
+}
diff --git a/optimizer/evaluator/evaluator_test.go b/optimizer/evaluator/evaluator_test.go
index 573d6ad376..097315ff98 100644
--- a/optimizer/evaluator/evaluator_test.go
+++ b/optimizer/evaluator/evaluator_test.go
@@ -1054,3 +1054,27 @@ func (s *testEvaluatorSuite) TestColumnNameExpr(c *C) {
 	c.Assert(err, IsNil)
 	c.Assert(result, Equals, 2)
 }
+
+func (s *testEvaluatorSuite) TestAggFuncAvg(c *C) {
+	ctx := mock.NewContext()
+	avg := &ast.AggregateFuncExpr{
+		F: ast.AggFuncAvg,
+	}
+	avg.CurrentGroup = "emptyGroup"
+	result, err := Eval(ctx, avg)
+	c.Assert(err, IsNil)
+	// Empty group should return nil.
+	c.Assert(result, IsNil)
+
+	avg.Args = []ast.ExprNode{ast.NewValueExpr(2)}
+	avg.Update()
+	avg.Args = []ast.ExprNode{ast.NewValueExpr(4)}
+	avg.Update()
+
+	result, err = Eval(ctx, avg)
+	c.Assert(err, IsNil)
+	expect, _ := mysql.ConvertToDecimal(3)
+	v, ok := result.(mysql.Decimal)
+	c.Assert(ok, IsTrue)
+	c.Assert(v.Equals(expect), IsTrue)
+}
diff --git a/optimizer/optimizer.go b/optimizer/optimizer.go
index b06748983a..c803b62abf 100644
--- a/optimizer/optimizer.go
+++ b/optimizer/optimizer.go
@@ -65,18 +65,10 @@ type supportChecker struct {
 }
 
 func (c *supportChecker) Enter(in ast.Node) (ast.Node, bool) {
-	switch ti := in.(type) {
+	switch x := in.(type) {
 	case *ast.SubqueryExpr:
 		c.unsupported = true
-	case *ast.AggregateFuncExpr:
-		fn := strings.ToLower(ti.F)
-		switch fn {
-		case ast.AggFuncCount, ast.AggFuncMax, ast.AggFuncMin, ast.AggFuncSum, ast.AggFuncGroupConcat:
-		default:
-			c.unsupported = true
-		}
 	case *ast.Join:
-		x := in.(*ast.Join)
 		if x.Right != nil {
 			c.unsupported = true
 		} else {
@@ -93,7 +85,6 @@ func (c *supportChecker) Enter(in ast.Node) (ast.Node, bool) {
 			}
 		}
 	case *ast.SelectStmt:
-		x := in.(*ast.SelectStmt)
 		if x.Distinct {
 			c.unsupported = true
 		}
@@ -123,25 +114,28 @@ func IsSupported(node ast.Node) bool {
 
 // Optimizer error codes.
 const (
-	CodeOneColumn     terror.ErrCode = 1
-	CodeSameColumns                  = 2
-	CodeMultiWildCard                = 3
-	CodeUnsupported                  = 4
+	CodeOneColumn           terror.ErrCode = 1
+	CodeSameColumns         terror.ErrCode = 2
+	CodeMultiWildCard       terror.ErrCode = 3
+	CodeUnsupported         terror.ErrCode = 4
+	CodeInvalidGroupFuncUse terror.ErrCode = 5
 )
 
 // Optimizer base errors.
 var (
-	ErrOneColumn     = terror.ClassOptimizer.New(CodeOneColumn, "Operand should contain 1 column(s)")
-	ErrSameColumns   = terror.ClassOptimizer.New(CodeSameColumns, "Operands should contain same columns")
-	ErrMultiWildCard = terror.ClassOptimizer.New(CodeMultiWildCard, "wildcard field exist more than once")
-	ErrUnSupported   = terror.ClassOptimizer.New(CodeUnsupported, "unsupported")
+	ErrOneColumn           = terror.ClassOptimizer.New(CodeOneColumn, "Operand should contain 1 column(s)")
+	ErrSameColumns         = terror.ClassOptimizer.New(CodeSameColumns, "Operands should contain same columns")
+	ErrMultiWildCard       = terror.ClassOptimizer.New(CodeMultiWildCard, "wildcard field exist more than once")
+	ErrUnSupported         = terror.ClassOptimizer.New(CodeUnsupported, "unsupported")
+	ErrInvalidGroupFuncUse = terror.ClassOptimizer.New(CodeInvalidGroupFuncUse, "Invalid use of group function")
 )
 
 func init() {
 	mySQLErrCodes := map[terror.ErrCode]uint16{
-		CodeOneColumn:     mysql.ErrOperandColumns,
-		CodeSameColumns:   mysql.ErrOperandColumns,
-		CodeMultiWildCard: mysql.ErrParse,
+		CodeOneColumn:           mysql.ErrOperandColumns,
+		CodeSameColumns:         mysql.ErrOperandColumns,
+		CodeMultiWildCard:       mysql.ErrParse,
+		CodeInvalidGroupFuncUse: mysql.ErrInvalidGroupFuncUse,
 	}
 	terror.ErrClassToMySQLCodes[terror.ClassOptimizer] = mySQLErrCodes
 }
diff --git a/optimizer/typeinferer.go b/optimizer/typeinferer.go
index 76d0479760..9e6a4bfd52 100644
--- a/optimizer/typeinferer.go
+++ b/optimizer/typeinferer.go
@@ -135,7 +135,7 @@ func (v *typeInferrer) aggregateFunc(x *ast.AggregateFuncExpr) {
 		x.SetType(ft)
 	case ast.AggFuncMax, ast.AggFuncMin:
 		x.SetType(x.Args[0].GetType())
-	case ast.AggFuncSum:
+	case ast.AggFuncSum, ast.AggFuncAvg:
 		ft := types.NewFieldType(mysql.TypeNewDecimal)
 		ft.Charset = charset.CharsetBin
 		ft.Collate = charset.CollationBin
diff --git a/optimizer/validator.go b/optimizer/validator.go
index ea9f208cc3..39ec3e3105 100644
--- a/optimizer/validator.go
+++ b/optimizer/validator.go
@@ -32,14 +32,26 @@ type validator struct {
 	err           error
 	wildCardCount int
 	inPrepare     bool
+	inAggregate   bool
 }
 
 func (v *validator) Enter(in ast.Node) (out ast.Node, skipChildren bool) {
+	switch in.(type) {
+	case *ast.AggregateFuncExpr:
+		if v.inAggregate {
+			// Aggregate function can not contain aggregate function.
+			v.err = ErrInvalidGroupFuncUse
+			return in, true
+		}
+		v.inAggregate = true
+	}
 	return in, false
 }
 
 func (v *validator) Leave(in ast.Node) (out ast.Node, ok bool) {
 	switch x := in.(type) {
+	case *ast.AggregateFuncExpr:
+		v.inAggregate = false
 	case *ast.BetweenExpr:
 		v.checkAllOneColumn(x.Expr, x.Left, x.Right)
 	case *ast.BinaryOperationExpr:
diff --git a/session.go b/session.go
index 98f065babb..c01266fa6f 100644
--- a/session.go
+++ b/session.go
@@ -554,6 +554,18 @@ func (s *session) Auth(user string, auth []byte, salt []byte) bool {
 	name := strs[0]
 	host := strs[1]
 	pwd, err := s.getPassword(name, host)
+	if err != nil {
+		if terror.ExecResultIsEmpty.Equal(err) {
+			log.Errorf("User [%s] not exist %v", name, err)
+		} else {
+			log.Errorf("Get User [%s] password from SystemDB error %v", name, err)
+		}
+		return false
+	}
+	if len(pwd) != 0 && len(pwd) != 40 {
+		log.Errorf("User [%s] password from SystemDB not like a sha1sum", name)
+		return false
+	}
 	hpwd, err := util.DecodePassword(pwd)
 	if err != nil {
 		log.Errorf("Decode password string error %v", err)
diff --git a/session_test.go b/session_test.go
index 46002e74b9..ef941da48e 100644
--- a/session_test.go
+++ b/session_test.go
@@ -1326,6 +1326,13 @@ func (s *testSessionSuite) TestSession(c *C) {
 	c.Assert(err, IsNil)
 }
 
+func (s *testSessionSuite) TestSessionAuth(c *C) {
+	store := newStore(c, s.dbName)
+	se := newSession(c, store, s.dbName)
+	defer se.Close()
+	c.Assert(se.Auth("Any not exist username with zero password! @anyhost", []byte(""), []byte("")), IsFalse)
+}
+
 func (s *testSessionSuite) TestErrorRollback(c *C) {
 	store := newStore(c, s.dbName)
 	s1 := newSession(c, store, s.dbName)