diff --git a/expression/builtin_time.go b/expression/builtin_time.go
index 2c1a9191f1..05f143507f 100644
--- a/expression/builtin_time.go
+++ b/expression/builtin_time.go
@@ -2005,9 +2005,6 @@ func (b *builtinStrToDateDurationSig) evalDuration(row chunk.Row) (types.Duratio
 	if !succ {
 		return types.Duration{}, true, handleInvalidTimeError(b.ctx, types.ErrWrongValue.GenWithStackByArgs(types.DateTimeStr, t.String()))
 	}
-	if b.ctx.GetSessionVars().SQLMode.HasNoZeroDateMode() && (t.Year() == 0 || t.Month() == 0 || t.Day() == 0) {
-		return types.Duration{}, true, handleInvalidTimeError(b.ctx, types.ErrWrongValue.GenWithStackByArgs(types.DateTimeStr, t.String()))
-	}
 	t.SetFsp(int8(b.tp.Decimal))
 	dur, err := t.ConvertToDuration()
 	return dur, err != nil, err
diff --git a/expression/integration_test.go b/expression/integration_test.go
index c087156faf..fae9ecdf93 100644
--- a/expression/integration_test.go
+++ b/expression/integration_test.go
@@ -1938,13 +1938,28 @@ func (s *testIntegrationSuite2) TestTimeBuiltin(c *C) {
 	result.Check(testkit.Rows("2017-01-01 2017-01-01 12:20:59 12:20:59"))
 	result = tk.MustQuery("select str_to_date('aaa01-01-2017', 'aaa%d-%m-%Y'), str_to_date('59:20:12 aaa01-01-2017', '%s:%i:%H aaa%d-%m-%Y'), str_to_date('59:20:12aaa', '%s:%i:%Haaa')")
 	result.Check(testkit.Rows("2017-01-01 2017-01-01 12:20:59 12:20:59"))
+
 	result = tk.MustQuery("select str_to_date('01-01-2017', '%d'), str_to_date('59', '%d-%Y')")
 	// TODO: MySQL returns "<nil> <nil>".
 	result.Check(testkit.Rows("0000-00-01 <nil>"))
-	tk.MustQuery("show warnings").Check(testutil.RowsWithSep("|", "Warning|1292|Incorrect datetime value: '0000-00-00 00:00:00'"))
+	result = tk.MustQuery("show warnings")
+	result.Sort().Check(testutil.RowsWithSep("|",
+		"Warning|1292|Incorrect datetime value: '0000-00-00 00:00:00'",
+		"Warning|1292|Truncated incorrect datetime value: '01-01-2017'"))
+
 	result = tk.MustQuery("select str_to_date('2018-6-1', '%Y-%m-%d'), str_to_date('2018-6-1', '%Y-%c-%d'), str_to_date('59:20:1', '%s:%i:%k'), str_to_date('59:20:1', '%s:%i:%l')")
 	result.Check(testkit.Rows("2018-06-01 2018-06-01 01:20:59 01:20:59"))
 
+	result = tk.MustQuery("select str_to_date('2020-07-04 11:22:33 PM c', '%Y-%m-%d %r')")
+	result.Check(testkit.Rows("2020-07-04 23:22:33"))
+	result = tk.MustQuery("show warnings")
+	result.Check(testutil.RowsWithSep("|", "Warning|1292|Truncated incorrect datetime value: '2020-07-04 11:22:33 PM c'"))
+
+	result = tk.MustQuery("select str_to_date('11:22:33 PM', ' %r')")
+	result.Check(testkit.Rows("23:22:33"))
+	result = tk.MustQuery("show warnings")
+	result.Check(testkit.Rows())
+
 	// for maketime
 	tk.MustExec(`drop table if exists t`)
 	tk.MustExec(`create table t(a double, b float, c decimal(10,4));`)
diff --git a/types/time.go b/types/time.go
index d97cc55958..0b8312386d 100644
--- a/types/time.go
+++ b/types/time.go
@@ -2678,7 +2678,8 @@ func abbrDayOfMonth(day int) string {
 func (t *Time) StrToDate(sc *stmtctx.StatementContext, date, format string) bool {
 	ctx := make(map[string]int)
 	var tm CoreTime
-	if !strToDate(&tm, date, format, ctx) {
+	success, warning := strToDate(&tm, date, format, ctx)
+	if !success {
 		t.SetCoreTime(ZeroCoreTime)
 		t.SetType(mysql.TypeDatetime)
 		t.SetFsp(0)
@@ -2690,7 +2691,15 @@ func (t *Time) StrToDate(sc *stmtctx.StatementContext, date, format string) bool
 
 	t.SetCoreTime(tm)
 	t.SetType(mysql.TypeDatetime)
-	return t.check(sc) == nil
+	if t.check(sc) != nil {
+		return false
+	}
+	if warning {
+		// Only append this warning when success but still need warning.
+		// Currently this only happens when `date` has extra characters at the end.
+		sc.AppendWarning(ErrTruncatedWrongVal.GenWithStackByArgs(DateTimeStr, date))
+	}
+	return true
 }
 
 // mysqlTimeFix fixes the Time use the values in the context.
@@ -2728,30 +2737,35 @@ func mysqlTimeFix(t *CoreTime, ctx map[string]int) error {
 	return nil
 }
 
-// strToDate converts date string according to format, returns true on success,
+// strToDate converts date string according to format,
 // the value will be stored in argument t or ctx.
-func strToDate(t *CoreTime, date string, format string, ctx map[string]int) bool {
+// The second return value is true when success but still need to append a warning.
+func strToDate(t *CoreTime, date string, format string, ctx map[string]int) (success bool, warning bool) {
 	date = skipWhiteSpace(date)
 	format = skipWhiteSpace(format)
 
 	token, formatRemain, succ := getFormatToken(format)
 	if !succ {
-		return false
+		return false, false
 	}
 
 	if token == "" {
-		// Extra characters at the end of date are ignored.
-		return true
+		if len(date) != 0 {
+			// Extra characters at the end of date are ignored, but a warning should be reported at this case.
+			return true, true
+		}
+		// Normal case. Both token and date are empty now.
+		return true, false
 	}
 
 	if len(date) == 0 {
 		ctx[token] = 0
-		return true
+		return true, false
 	}
 
 	dateRemain, succ := matchDateWithToken(t, date, token, ctx)
 	if !succ {
-		return false
+		return false, false
 	}
 
 	return strToDate(t, dateRemain, formatRemain, ctx)
@@ -2948,8 +2962,10 @@ func time12Hour(t *CoreTime, input string, ctx map[string]int) (string, bool) {
 	switch {
 	case strings.HasPrefix(remain, "AM"):
 		t.setHour(uint8(hour))
+		remain = strings.TrimPrefix(remain, "AM")
 	case strings.HasPrefix(remain, "PM"):
 		t.setHour(uint8(hour + 12))
+		remain = strings.TrimPrefix(remain, "PM")
 	default:
 		return input, false
 	}