diff --git a/fe/fe-core/src/test/java/org/apache/doris/nereids/rules/rewrite/NormalizeSortTest.java b/fe/fe-core/src/test/java/org/apache/doris/nereids/rules/rewrite/NormalizeSortTest.java
new file mode 100644
index 0000000000..a2bd55092b
--- /dev/null
+++ b/fe/fe-core/src/test/java/org/apache/doris/nereids/rules/rewrite/NormalizeSortTest.java
@@ -0,0 +1,73 @@
+// Licensed to the Apache Software Foundation (ASF) under one
+// or more contributor license agreements.  See the NOTICE file
+// distributed with this work for additional information
+// regarding copyright ownership.  The ASF licenses this file
+// to you under the Apache License, Version 2.0 (the
+// "License"); you may not use this file except in compliance
+// with the License.  You may obtain a copy of the License at
+//
+//   http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing,
+// software distributed under the License is distributed on an
+// "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+// KIND, either express or implied.  See the License for the
+// specific language governing permissions and limitations
+// under the License.
+
+package org.apache.doris.nereids.rules.rewrite;
+
+import org.apache.doris.nereids.properties.OrderKey;
+import org.apache.doris.nereids.trees.expressions.Add;
+import org.apache.doris.nereids.trees.expressions.Alias;
+import org.apache.doris.nereids.trees.expressions.Expression;
+import org.apache.doris.nereids.trees.expressions.StatementScopeIdGenerator;
+import org.apache.doris.nereids.trees.expressions.literal.IntegerLiteral;
+import org.apache.doris.nereids.trees.plans.logical.LogicalOlapScan;
+import org.apache.doris.nereids.trees.plans.logical.LogicalPlan;
+import org.apache.doris.nereids.util.LogicalPlanBuilder;
+import org.apache.doris.nereids.util.MemoPatternMatchSupported;
+import org.apache.doris.nereids.util.MemoTestUtils;
+import org.apache.doris.nereids.util.PlanChecker;
+import org.apache.doris.nereids.util.PlanConstructor;
+
+import com.google.common.collect.Lists;
+import org.junit.jupiter.api.Test;
+
+import java.util.List;
+
+/**
+ * NormalizeSortTest ut
+ */
+class NormalizeSortTest implements MemoPatternMatchSupported {
+    LogicalOlapScan score = new LogicalOlapScan(StatementScopeIdGenerator.newRelationId(), PlanConstructor.score);
+
+    @Test
+    void testOrderByExpr() {
+        Expression add = new Add(score.getOutput().get(0), new IntegerLiteral(1));
+        List<OrderKey> orderKeys = Lists.newArrayList(new OrderKey(add, true, true));
+        LogicalPlan plan = new LogicalPlanBuilder(score)
+                .sort(orderKeys)
+                .build();
+        PlanChecker.from(MemoTestUtils.createConnectContext(), plan)
+                .applyTopDown(new NormalizeSort())
+                .matches(logicalProject(logicalSort(logicalProject().when(p -> p.getProjects().stream().anyMatch(e -> e.toSql().contains(
+                        add.toSql())))))
+                        .when(p -> p.getOutput().equals(plan.getOutput())));
+    }
+
+    @Test
+    void testOrderByAlias() {
+        Expression add = new Add(score.getOutput().get(0), new IntegerLiteral(1));
+        Expression alias = new Alias(add);
+        List<OrderKey> orderKeys = Lists.newArrayList(new OrderKey(alias, true, true));
+        LogicalPlan plan = new LogicalPlanBuilder(score)
+                .sort(orderKeys)
+                .build();
+        PlanChecker.from(MemoTestUtils.createConnectContext(), plan)
+                .applyTopDown(new NormalizeSort())
+                .matches(logicalProject(logicalSort(logicalProject().when(p -> p.getProjects().stream().anyMatch(e -> e.toSql().contains(
+                        alias.toSql())))))
+                        .when(p -> p.getOutput().equals(plan.getOutput())));
+    }
+}