diff --git a/samtranslator/swagger/swagger.py b/samtranslator/swagger/swagger.py
index abd15b92c5..1e79961a87 100644
--- a/samtranslator/swagger/swagger.py
+++ b/samtranslator/swagger/swagger.py
@@ -1144,4 +1144,5 @@ def safe_compare_regex_with_string(regex, data):
 
     @staticmethod
     def get_path_without_trailing_slash(path):
-        return re.sub(r"{([a-zA-Z0-9._-]+|proxy\+)}", "*", path)
+        # convert greedy paths to such as {greedy+}, {proxy+} to "*"
+        return re.sub(r"{([a-zA-Z0-9._-]+|[a-zA-Z0-9._-]+\+|proxy\+)}", "*", path)
diff --git a/tests/model/eventsources/test_api_event_source.py b/tests/model/eventsources/test_api_event_source.py
index 040e0aba0d..6357e1d69d 100644
--- a/tests/model/eventsources/test_api_event_source.py
+++ b/tests/model/eventsources/test_api_event_source.py
@@ -51,6 +51,23 @@ def test_get_permission_with_trailing_slash(self):
 
         self.assertEqual(arn, "arn:aws:execute-api:${AWS::Region}:${AWS::AccountId}:${__ApiId__}/${__Stage__}/GET/foo")
 
+    @patch("boto3.session.Session.region_name", "eu-west-2")
+    def test_get_permission_with_path_parameter_to_any_path(self):
+        self.api_event_source.Path = "/foo/{userId+}"
+        cfn = self.api_event_source.to_cloudformation(function=self.func, explicit_api={})
+
+        perm = cfn[0]
+        self.assertIsInstance(perm, LambdaPermission)
+
+        try:
+            arn = self._extract_path_from_arn("{}PermissionProd".format(self.logical_id), perm)
+        except AttributeError:
+            self.fail("Permission class isn't valid")
+
+        self.assertEqual(
+            arn, "arn:aws:execute-api:${AWS::Region}:${AWS::AccountId}:${__ApiId__}/${__Stage__}/GET/foo/*"
+        )
+
     @patch("boto3.session.Session.region_name", "eu-west-2")
     def test_get_permission_with_path_parameter(self):
         self.api_event_source.Path = "/foo/{userId}/bar"