diff --git a/onnxscript/optimizer/_constant_folding_test.py b/onnxscript/optimizer/_constant_folding_test.py
index ae5c9901b..080af9c2f 100644
--- a/onnxscript/optimizer/_constant_folding_test.py
+++ b/onnxscript/optimizer/_constant_folding_test.py
@@ -741,6 +741,31 @@ def test_constant_folding_creates_constant_nodes_in_function(self):
             constant_nodes = [n for n in func.graph if n.op_type == "Constant"]
             self.assertEqual(len(constant_nodes), 1)
 
+    def test_initializer_as_graph_output_is_not_removed(self):
+        """Test that an initializer that is a graph output is not removed during constant folding."""
+        model = """
+            <ir_version: 7, opset_import: [ "" : 17]>
+            agraph (float[N] x) => (float[N] y, float z) {
+                constant = Constant <value_float=2.0> ()
+                y = Mul(x, constant)
+                z = Identity(constant)
+            }
+        """
+
+        optimized = self._fold(model)
+        # After constant folding, the Identity node should be folded, and 'constant'
+        # should become an initializer with the output name 'z'.
+        # The key thing is that this initializer should NOT be removed even though
+        # the Identity node was folded, because it is a graph output.
+        self.assertIn("z", optimized.graph.initializers)
+        # The Identity node should be removed
+        identity_nodes = [n for n in optimized.graph if n.op_type == "Identity"]
+        self.assertEqual(len(identity_nodes), 0)
+        # Verify the graph still has both outputs
+        output_names = [o.name for o in optimized.graph.outputs]
+        self.assertIn("y", output_names)
+        self.assertIn("z", output_names)
+
 
 if __name__ == "__main__":
     unittest.main()