diff --git a/cinder/backup/drivers/posix.py b/cinder/backup/drivers/posix.py
index b7f151b25..d6accc035 100644
--- a/cinder/backup/drivers/posix.py
+++ b/cinder/backup/drivers/posix.py
@@ -23,6 +23,7 @@ import stat
 
 from oslo_config import cfg
 from oslo_log import log as logging
+from oslo_utils import timeutils
 
 from cinder.backup import chunkeddriver
 from cinder import exception
@@ -129,7 +130,11 @@ class PosixBackupDriver(chunkeddriver.ChunkedBackupDriver):
         os.remove(path)
 
     def _generate_object_name_prefix(self, backup):
-        return 'backup'
+        timestamp = timeutils.utcnow().strftime("%Y%m%d%H%M%S")
+        prefix = 'volume_%s_%s_backup_%s' % (backup.volume_id, timestamp,
+                                             backup.id)
+        LOG.debug('_generate_object_name_prefix: %s', prefix)
+        return prefix
 
     def get_extra_metadata(self, backup, volume):
         return None
diff --git a/cinder/tests/unit/backup/drivers/test_backup_posix.py b/cinder/tests/unit/backup/drivers/test_backup_posix.py
index 1b86bad4f..ff3a21dd7 100644
--- a/cinder/tests/unit/backup/drivers/test_backup_posix.py
+++ b/cinder/tests/unit/backup/drivers/test_backup_posix.py
@@ -24,6 +24,7 @@ from six.moves import builtins
 
 from cinder.backup.drivers import posix
 from cinder import context
+from cinder import objects
 from cinder import test
 from cinder.tests.unit import fake_constants as fake
 
@@ -180,3 +181,15 @@ class PosixBackupDriverTestCase(test.TestCase):
         self.assertRaises(OSError,
                           self.driver.delete_object, FAKE_CONTAINER,
                           FAKE_OBJECT_NAME)
+
+    @mock.patch.object(posix.timeutils, 'utcnow')
+    def test_generate_object_name_prefix(self, utcnow_mock):
+        timestamp = '20170518102205'
+        utcnow_mock.return_value.strftime.return_value = timestamp
+        backup = objects.Backup(self.ctxt, volume_id=fake.VOLUME_ID,
+                                id=fake.BACKUP_ID)
+        res = self.driver._generate_object_name_prefix(backup)
+        expected = 'volume_%s_%s_backup_%s' % (backup.volume_id,
+                                               timestamp,
+                                               backup.id)
+        self.assertEqual(expected, res)
diff --git a/releasenotes/notes/nfs_backup_no_overwrite-be7b545453baf7a3.yaml b/releasenotes/notes/nfs_backup_no_overwrite-be7b545453baf7a3.yaml
new file mode 100644
index 000000000..73227a65c
--- /dev/null
+++ b/releasenotes/notes/nfs_backup_no_overwrite-be7b545453baf7a3.yaml
@@ -0,0 +1,5 @@
+---
+fixes:
+  - |
+    Fix NFS backup driver, we now support multiple backups on the same
+    container, they are no longer overwritten.