diff --git a/IMPLEMENTATION_COVERAGE.md b/IMPLEMENTATION_COVERAGE.md
index a5650f572..1c76b04cf 100644
--- a/IMPLEMENTATION_COVERAGE.md
+++ b/IMPLEMENTATION_COVERAGE.md
@@ -2334,7 +2334,7 @@
 - [ ] update_service_specific_credential
 - [X] update_signing_certificate
 - [ ] update_ssh_public_key
-- [ ] update_user
+- [X] update_user
 - [X] upload_server_certificate
 - [X] upload_signing_certificate
 - [ ] upload_ssh_public_key
diff --git a/moto/iam/models.py b/moto/iam/models.py
index 92ac19da7..ae993ebfd 100644
--- a/moto/iam/models.py
+++ b/moto/iam/models.py
@@ -892,6 +892,18 @@ class IAMBackend(BaseBackend):
 
         return users
 
+    def update_user(self, user_name, new_path=None, new_user_name=None):
+        try:
+            user = self.users[user_name]
+        except KeyError:
+            raise IAMNotFoundException("User {0} not found".format(user_name))
+
+        if new_path:
+            user.path = new_path
+        if new_user_name:
+            user.name = new_user_name
+            self.users[new_user_name] = self.users.pop(user_name)
+
     def list_roles(self, path_prefix, marker, max_items):
         roles = None
         try:
diff --git a/moto/iam/responses.py b/moto/iam/responses.py
index 5b19c9cdc..e5b4c9070 100644
--- a/moto/iam/responses.py
+++ b/moto/iam/responses.py
@@ -440,6 +440,18 @@ class IamResponse(BaseResponse):
         template = self.response_template(LIST_USERS_TEMPLATE)
         return template.render(action='List', users=users)
 
+    def update_user(self):
+        user_name = self._get_param('UserName')
+        new_path = self._get_param('NewPath')
+        new_user_name = self._get_param('NewUserName')
+        iam_backend.update_user(user_name, new_path, new_user_name)
+        if new_user_name:
+            user = iam_backend.get_user(new_user_name)
+        else:
+            user = iam_backend.get_user(user_name)
+        template = self.response_template(USER_TEMPLATE)
+        return template.render(action='Update', user=user)
+
     def create_login_profile(self):
         user_name = self._get_param('UserName')
         password = self._get_param('Password')
diff --git a/tests/test_iam/test_iam.py b/tests/test_iam/test_iam.py
index ceec5e06a..5875b747a 100644
--- a/tests/test_iam/test_iam.py
+++ b/tests/test_iam/test_iam.py
@@ -401,6 +401,19 @@ def test_get_user():
     conn.get_user('my-user')
 
 
+@mock_iam()
+def test_update_user():
+    conn = boto3.client('iam', region_name='us-east-1')
+    with assert_raises(conn.exceptions.NoSuchEntityException):
+        conn.update_user(UserName='my-user')
+    conn.create_user(UserName='my-user')
+    conn.update_user(UserName='my-user', NewPath='/new-path/', NewUserName='new-user')
+    response = conn.get_user(UserName='new-user')
+    response['User'].get('Path').should.equal('/new-path/')
+    with assert_raises(conn.exceptions.NoSuchEntityException):
+        conn.get_user(UserName='my-user')
+
+
 @mock_iam_deprecated()
 def test_get_current_user():
     """If no user is specific, IAM returns the current user"""