diff --git a/fe/fe-core/src/main/java/org/apache/doris/nereids/properties/OrderKey.java b/fe/fe-core/src/main/java/org/apache/doris/nereids/properties/OrderKey.java
index 7d6ee6eb8d..8059b2ddfa 100644
--- a/fe/fe-core/src/main/java/org/apache/doris/nereids/properties/OrderKey.java
+++ b/fe/fe-core/src/main/java/org/apache/doris/nereids/properties/OrderKey.java
@@ -19,6 +19,8 @@ package org.apache.doris.nereids.properties;
 
 import org.apache.doris.nereids.trees.expressions.Expression;
 
+import java.util.Objects;
+
 /**
  * Represents the order key of a statement.
  */
@@ -67,4 +69,21 @@ public class OrderKey {
     public String toString() {
         return expr.toSql();
     }
+
+    @Override
+    public int hashCode() {
+        return Objects.hash(expr, isAsc, nullFirst);
+    }
+
+    @Override
+    public boolean equals(Object o) {
+        if (this == o) {
+            return true;
+        }
+        if (o == null || getClass() != o.getClass()) {
+            return false;
+        }
+        OrderKey that = (OrderKey) o;
+        return isAsc == that.isAsc() && nullFirst == that.isNullFirst() && expr.equals(that.getExpr());
+    }
 }