diff --git a/cinder/api/contrib/backups.py b/cinder/api/contrib/backups.py
index 261d6287dfc..a23a65b3d74 100644
--- a/cinder/api/contrib/backups.py
+++ b/cinder/api/contrib/backups.py
@@ -87,6 +87,10 @@ class BackupsController(wsgi.Controller):
                                             filters,
                                             self._get_backup_filter_options())
 
+    def _convert_sort_name(self, req_version, sort_keys):
+        """Convert sort key "name" to "display_name". """
+        pass
+
     def _get_backups(self, req, is_detail):
         """Returns a list of backups, transformed through view builder."""
         context = req.environ['cinder.context']
@@ -95,6 +99,7 @@ class BackupsController(wsgi.Controller):
         marker, limit, offset = common.get_pagination_params(filters)
         sort_keys, sort_dirs = common.get_sort_params(filters)
 
+        self._convert_sort_name(req_version, sort_keys)
         self._process_backup_filtering(context=context, filters=filters,
                                        req_version=req_version)
 
diff --git a/cinder/api/openstack/api_version_request.py b/cinder/api/openstack/api_version_request.py
index 7bc492d971c..4d229f08bc0 100644
--- a/cinder/api/openstack/api_version_request.py
+++ b/cinder/api/openstack/api_version_request.py
@@ -90,6 +90,7 @@ REST_API_VERSION_HISTORY = """
              list APIs.
     * 3.35 - Add ``volume-type`` filter to Get-Pools API.
     * 3.36 - Add metadata to volumes/summary response body.
+    * 3.37 - Support sort backup by "name".
 """
 
 # The minimum and maximum versions of the API supported
@@ -97,7 +98,7 @@ REST_API_VERSION_HISTORY = """
 # minimum version of the API supported.
 # Explicitly using /v1 or /v2 endpoints will still work
 _MIN_API_VERSION = "3.0"
-_MAX_API_VERSION = "3.36"
+_MAX_API_VERSION = "3.37"
 _LEGACY_API_VERSION1 = "1.0"
 _LEGACY_API_VERSION2 = "2.0"
 
diff --git a/cinder/api/openstack/rest_api_version_history.rst b/cinder/api/openstack/rest_api_version_history.rst
index 3de8d56b4de..e1045c5f408 100644
--- a/cinder/api/openstack/rest_api_version_history.rst
+++ b/cinder/api/openstack/rest_api_version_history.rst
@@ -321,3 +321,7 @@ user documentation.
 3.36
 ----
   Add metadata to volumes/summary response body.
+
+3.37
+----
+  Support sort backup by "name".
diff --git a/cinder/api/v3/backups.py b/cinder/api/v3/backups.py
index d639fb2b948..5793a4cadd9 100644
--- a/cinder/api/v3/backups.py
+++ b/cinder/api/v3/backups.py
@@ -96,6 +96,10 @@ class BackupsController(backups_v2.BackupsController):
                 pass
         return resp_backup
 
+    def _convert_sort_name(self, req_version, sort_keys):
+        if req_version.matches("3.37") and 'name' in sort_keys:
+            sort_keys[sort_keys.index('name')] = 'display_name'
+
 
 def create_resource():
     return wsgi.Resource(BackupsController())
diff --git a/cinder/tests/unit/api/v3/test_backups.py b/cinder/tests/unit/api/v3/test_backups.py
index 2bf9e0d16fe..33fdabae805 100644
--- a/cinder/tests/unit/api/v3/test_backups.py
+++ b/cinder/tests/unit/api/v3/test_backups.py
@@ -21,6 +21,7 @@ import webob
 
 from cinder.api.openstack import api_version_request as api_version
 from cinder.api.v3 import backups
+from cinder.api.views import backups as backup_view
 import cinder.backup
 from cinder import context
 from cinder import exception
@@ -100,6 +101,26 @@ class BackupsControllerAPITestCase(test.TestCase):
                                                 mock.ANY, 'backup',
                                                 support_like)
 
+    @ddt.data('3.36', '3.37')
+    def test_backup_list_with_name(self, version):
+        backup1 = test_utils.create_backup(
+            self.ctxt, display_name='b_test_name',
+            status=fields.BackupStatus.AVAILABLE)
+        backup2 = test_utils.create_backup(
+            self.ctxt, display_name='a_test_name',
+            status=fields.BackupStatus.AVAILABLE)
+        url = '/v3/%s/backups?sort_key=name' % fake.PROJECT_ID
+        req = fakes.HTTPRequest.blank(url, version=version)
+        if version == '3.36':
+            self.assertRaises(exception.InvalidInput,
+                              self.controller.index,
+                              req)
+        else:
+            expect = backup_view.ViewBuilder().summary_list(req,
+                                                            [backup1, backup2])
+            result = self.controller.index(req)
+            self.assertEqual(expect, result)
+
     def test_backup_update(self):
         backup = test_utils.create_backup(
             self.ctxt,
diff --git a/releasenotes/notes/support_sort_backup_by_name-0b080bcb60c0eaa0.yaml b/releasenotes/notes/support_sort_backup_by_name-0b080bcb60c0eaa0.yaml
new file mode 100644
index 00000000000..79d56362915
--- /dev/null
+++ b/releasenotes/notes/support_sort_backup_by_name-0b080bcb60c0eaa0.yaml
@@ -0,0 +1,3 @@
+---
+features:
+  - Add support for sorting backups by "name".
\ No newline at end of file