diff --git a/onnxscript/version_converter/_version_converter.py b/onnxscript/version_converter/_version_converter.py
index 7470df0ead..7281318619 100644
--- a/onnxscript/version_converter/_version_converter.py
+++ b/onnxscript/version_converter/_version_converter.py
@@ -34,11 +34,11 @@ def _get_onnx_opset_version(model: ir.Model) -> int | None:
     return model_version1 or model_version2
 
 
-def _set_onnx_opset_version(model: ir.Model, version: int) -> None:
-    """Set the ONNX opset version imported by the model."""
-    if "ai.onnx" in model.opset_imports:
-        del model.opset_imports["ai.onnx"]
-    model.opset_imports[""] = version
+def _set_onnx_opset_version(model_or_function: ir.Model | ir.Function, version: int) -> None:
+    """Set the ONNX opset version imported by the model or function."""
+    if "ai.onnx" in model_or_function.opset_imports:
+        del model_or_function.opset_imports["ai.onnx"]
+    model_or_function.opset_imports[""] = version
 
 
 class VersionConverterError(RuntimeError):
@@ -334,6 +334,7 @@ def visit_model(self, model: ir.Model) -> None:
         self.visit_graph_or_function(model.graph)
         for function in model.functions.values():
             self.visit_graph_or_function(function)
+            _set_onnx_opset_version(function, self._target_version)
         _set_onnx_opset_version(model, self._target_version)
 
 
diff --git a/onnxscript/version_converter/_version_converter_test.py b/onnxscript/version_converter/_version_converter_test.py
index 2b615a8f7f..bf481313f4 100644
--- a/onnxscript/version_converter/_version_converter_test.py
+++ b/onnxscript/version_converter/_version_converter_test.py
@@ -237,8 +237,11 @@ def test_version_convert_function_nodes(self):
         version_converter.convert_version(model, target_version=target_version)
         self.assertEqual(model.opset_imports[""], target_version)
 
-        # Verify that nodes inside the function were version-converted
+        # Verify that the function's opset_imports are updated
         func = model.functions[("pkg.custom", "dft_func", "")]
+        self.assertEqual(func.opset_imports[""], target_version)
+
+        # Verify that nodes inside the function were version-converted
         self.assertEqual(func[0].op_type, "Constant")
         self.assertEqual(func[0].version, 20)
         self.assertEqual(func[1].op_type, "Reshape")
@@ -293,8 +296,12 @@ def test_version_convert_function_with_control_flow_subgraph(self):
         version_converter.convert_version(model, target_version=target_version)
         self.assertEqual(model.opset_imports[""], target_version)
 
-        # Verify nodes inside the function's If node subgraphs were version-converted
+        # Verify that the function's opset_imports are updated
         func = model.functions[("pkg.custom", "conditional_dft", "")]
+        self.assertEqual(func.opset_imports[""], target_version)
+
+        # Verify nodes inside the function's If node subgraphs were version-converted
+        # Verify nodes inside the function's If node subgraphs were version-converted
         if_node = func[0]
         self.assertEqual(if_node.op_type, "If")
         self.assertEqual(if_node.version, 20)