diff --git a/sql/catalyst/src/main/scala/org/apache/spark/sql/catalyst/optimizer/Optimizer.scala b/sql/catalyst/src/main/scala/org/apache/spark/sql/catalyst/optimizer/Optimizer.scala
index c79fd7a87a83..f4da7870a132 100644
--- a/sql/catalyst/src/main/scala/org/apache/spark/sql/catalyst/optimizer/Optimizer.scala
+++ b/sql/catalyst/src/main/scala/org/apache/spark/sql/catalyst/optimizer/Optimizer.scala
@@ -647,6 +647,11 @@ object LimitPushDown extends Rule[LogicalPlan] {
     // There is a Project between LocalLimit and Join if they do not have the same output.
     case LocalLimit(exp, project @ Project(_, join: Join)) =>
       LocalLimit(exp, project.copy(child = pushLocalLimitThroughJoin(exp, join)))
+    // Push down limit 1 through Aggregate and turn Aggregate into Project if it is group only.
+    case Limit(le @ IntegerLiteral(1), a: Aggregate) if a.groupOnly =>
+      Limit(le, Project(a.output, LocalLimit(le, a.child)))
+    case Limit(le @ IntegerLiteral(1), p @ Project(_, a: Aggregate)) if a.groupOnly =>
+      Limit(le, p.copy(child = Project(a.output, LocalLimit(le, a.child))))
   }
 }
 
diff --git a/sql/catalyst/src/test/scala/org/apache/spark/sql/catalyst/optimizer/LimitPushdownSuite.scala b/sql/catalyst/src/test/scala/org/apache/spark/sql/catalyst/optimizer/LimitPushdownSuite.scala
index c2503e362c8c..848416b09813 100644
--- a/sql/catalyst/src/test/scala/org/apache/spark/sql/catalyst/optimizer/LimitPushdownSuite.scala
+++ b/sql/catalyst/src/test/scala/org/apache/spark/sql/catalyst/optimizer/LimitPushdownSuite.scala
@@ -239,4 +239,28 @@ class LimitPushdownSuite extends PlanTest {
       Limit(5, LocalLimit(5, x).join(y, LeftOuter, joinCondition).select("x.a".attr)).analyze
     comparePlans(optimized, correctAnswer)
   }
+
+  test("SPARK-36183: Push down limit 1 through Aggregate if it is group only") {
+    // Push down when it is group only and limit 1.
+    comparePlans(
+      Optimize.execute(x.groupBy("x.a".attr)("x.a".attr).limit(1).analyze),
+      LocalLimit(1, x).select("x.a".attr).limit(1).analyze)
+
+    comparePlans(
+      Optimize.execute(x.groupBy("x.a".attr)("x.a".attr).select("x.a".attr).limit(1).analyze),
+      LocalLimit(1, x).select("x.a".attr).select("x.a".attr).limit(1).analyze)
+
+    comparePlans(
+      Optimize.execute(x.union(y).groupBy("x.a".attr)("x.a".attr).limit(1).analyze),
+      LocalLimit(1, LocalLimit(1, x).union(LocalLimit(1, y))).select("x.a".attr).limit(1).analyze)
+
+    // No push down
+    comparePlans(
+      Optimize.execute(x.groupBy("x.a".attr)("x.a".attr).limit(2).analyze),
+      x.groupBy("x.a".attr)("x.a".attr).limit(2).analyze)
+
+    comparePlans(
+      Optimize.execute(x.groupBy("x.a".attr)("x.a".attr, count("x.a".attr)).limit(1).analyze),
+      x.groupBy("x.a".attr)("x.a".attr, count("x.a".attr)).limit(1).analyze)
+  }
 }