diff --git a/moto/iam/models.py b/moto/iam/models.py
index 5608a87d..b64c9402 100644
--- a/moto/iam/models.py
+++ b/moto/iam/models.py
@@ -1233,6 +1233,14 @@ class IAMBackend(BaseBackend):
         group = self.get_group(group_name)
         return group.get_policy(policy_name)
 
+    def delete_group(self, group_name):
+        try:
+            del self.groups[group_name]
+        except KeyError:
+            raise IAMNotFoundException(
+                "The group with name {0} cannot be found.".format(group_name)
+            )
+
     def create_user(self, user_name, path="/"):
         if user_name in self.users:
             raise IAMConflictException(
diff --git a/moto/iam/responses.py b/moto/iam/responses.py
index 08fe13dc..4bd1aa80 100644
--- a/moto/iam/responses.py
+++ b/moto/iam/responses.py
@@ -428,6 +428,12 @@ class IamResponse(BaseResponse):
         template = self.response_template(GET_GROUP_POLICY_TEMPLATE)
         return template.render(name="GetGroupPolicyResponse", **policy_result)
 
+    def delete_group(self):
+        group_name = self._get_param("GroupName")
+        iam_backend.delete_group(group_name)
+        template = self.response_template(GENERIC_EMPTY_TEMPLATE)
+        return template.render(name="DeleteGroup")
+
     def create_user(self):
         user_name = self._get_param("UserName")
         path = self._get_param("Path")
diff --git a/tests/test_iam/test_iam_groups.py b/tests/test_iam/test_iam_groups.py
index 7fd29928..7b73e89e 100644
--- a/tests/test_iam/test_iam_groups.py
+++ b/tests/test_iam/test_iam_groups.py
@@ -8,6 +8,7 @@ import sure  # noqa
 
 from nose.tools import assert_raises
 from boto.exception import BotoServerError
+from botocore.exceptions import ClientError
 from moto import mock_iam, mock_iam_deprecated
 
 MOCK_POLICY = """
@@ -182,3 +183,25 @@ def test_list_group_policies():
     conn.list_group_policies(GroupName="my-group")["PolicyNames"].should.equal(
         ["my-policy"]
     )
+
+
+@mock_iam
+def test_delete_group():
+    conn = boto3.client("iam", region_name="us-east-1")
+    conn.create_group(GroupName="my-group")
+    groups = conn.list_groups()
+    assert groups["Groups"][0]["GroupName"] == "my-group"
+    assert len(groups["Groups"]) == 1
+    conn.delete_group(GroupName="my-group")
+    conn.list_groups()["Groups"].should.be.empty
+
+
+@mock_iam
+def test_delete_unknown_group():
+    conn = boto3.client("iam", region_name="us-east-1")
+    with assert_raises(ClientError) as err:
+        conn.delete_group(GroupName="unknown-group")
+    err.exception.response["Error"]["Code"].should.equal("NoSuchEntity")
+    err.exception.response["Error"]["Message"].should.equal(
+        "The group with name unknown-group cannot be found."
+    )