diff --git a/IMPLEMENTATION_COVERAGE.md b/IMPLEMENTATION_COVERAGE.md
index 060f9f7a..4fd909d6 100644
--- a/IMPLEMENTATION_COVERAGE.md
+++ b/IMPLEMENTATION_COVERAGE.md
@@ -3194,7 +3194,7 @@
 - [ ] delete_instance_profile
 - [X] delete_login_profile
 - [ ] delete_open_id_connect_provider
-- [ ] delete_policy
+- [X] delete_policy
 - [X] delete_policy_version
 - [X] delete_role
 - [ ] delete_role_permissions_boundary
diff --git a/moto/iam/models.py b/moto/iam/models.py
index d76df8a2..506f2a94 100644
--- a/moto/iam/models.py
+++ b/moto/iam/models.py
@@ -1099,6 +1099,9 @@ class IAMBackend(BaseBackend):
         user = self.get_user(user_name)
         user.delete_policy(policy_name)
 
+    def delete_policy(self, policy_arn):
+        del self.managed_policies[policy_arn]
+
     def create_access_key(self, user_name=None):
         user = self.get_user(user_name)
         key = user.create_access_key()
diff --git a/moto/iam/responses.py b/moto/iam/responses.py
index 806dd37f..8e63c107 100644
--- a/moto/iam/responses.py
+++ b/moto/iam/responses.py
@@ -604,6 +604,12 @@ class IamResponse(BaseResponse):
         template = self.response_template(GENERIC_EMPTY_TEMPLATE)
         return template.render(name='DeleteUser')
 
+    def delete_policy(self):
+        policy_arn = self._get_param('PolicyArn')
+        iam_backend.delete_policy(policy_arn)
+        template = self.response_template(GENERIC_EMPTY_TEMPLATE)
+        return template.render(name='DeletePolicy')
+
     def delete_login_profile(self):
         user_name = self._get_param('UserName')
         iam_backend.delete_login_profile(user_name)
diff --git a/tests/test_awslambda/test_lambda_eventsourcemappings.py b/tests/test_awslambda/test_lambda_eventsourcemappings.py
new file mode 100644
index 00000000..e69de29b
diff --git a/tests/test_iam/test_iam.py b/tests/test_iam/test_iam.py
index fe2117a3..23846712 100644
--- a/tests/test_iam/test_iam.py
+++ b/tests/test_iam/test_iam.py
@@ -338,6 +338,15 @@ def test_create_policy():
     response['Policy']['Arn'].should.equal("arn:aws:iam::123456789012:policy/TestCreatePolicy")
 
 
+@mock_iam
+def test_delete_policy():
+    conn = boto3.client('iam', region_name='us-east-1')
+    response = conn.create_policy(PolicyName="TestCreatePolicy", PolicyDocument=MOCK_POLICY)
+    [pol['PolicyName'] for pol in conn.list_policies(Scope='Local')['Policies']].should.equal(['TestCreatePolicy'])
+    conn.delete_policy(PolicyArn=response['Policy']['Arn'])
+    assert conn.list_policies(Scope='Local')['Policies'].should.be.empty
+
+
 @mock_iam
 def test_create_policy_versions():
     conn = boto3.client('iam', region_name='us-east-1')
@@ -713,7 +722,7 @@ def test_mfa_devices():
 
 
 @mock_iam_deprecated()
-def test_delete_user():
+def test_delete_user_deprecated():
     conn = boto.connect_iam()
     with assert_raises(BotoServerError):
         conn.delete_user('my-user')
@@ -721,6 +730,17 @@ def test_delete_user():
     conn.delete_user('my-user')
 
 
+@mock_iam()
+def test_delete_user():
+    conn = boto3.client('iam', region_name='us-east-1')
+    with assert_raises(ClientError):
+        conn.delete_user(UserName='my-user')
+    conn.create_user(UserName='my-user')
+    [user['UserName'] for user in conn.list_users()['Users']].should.equal(['my-user'])
+    conn.delete_user(UserName='my-user')
+    assert conn.list_users()['Users'].should.be.empty
+
+
 @mock_iam_deprecated()
 def test_generate_credential_report():
     conn = boto.connect_iam()