diff --git a/CHANGELOG.md b/CHANGELOG.md
index 250b2ea76f6e..32763e073d37 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -10,6 +10,10 @@
 * [#896](https://github.com/bbatsov/rubocop/issues/896): New option `--fail-level` changes minimum severity for exit with error code. ([@hiroponz][])
 * `VariableInterpolation` cop does auto-correction. ([@bbatsov][])
 
+### Changes
+
+* [#913](https://github.com/bbatsov/rubocop/issues/913): `FileName` accepts multiple extensions. ([@tamird][])
+
 ### Bugs fixed
 
 * [#904](https://github.com/bbatsov/rubocop/issues/904): Fixed a NPE in `LiteralInInterpolation`. ([@bbatsov][])
@@ -794,3 +798,4 @@
 [@tmorris-fiksu]: https://github.com/tmorris-fiksu
 [@mockdeep]: https://github.com/mockdeep
 [@hiroponz]: https://github.com/hiroponz
+[@tamird]: https://github.com/tamird
diff --git a/lib/rubocop/cop/style/file_name.rb b/lib/rubocop/cop/style/file_name.rb
index 399b4c2043f5..c37f76fff26b 100644
--- a/lib/rubocop/cop/style/file_name.rb
+++ b/lib/rubocop/cop/style/file_name.rb
@@ -16,7 +16,7 @@ def investigate(processed_source)
 
           basename = File.basename(file_path).sub(/\.[^\.]+$/, '')
 
-          unless basename =~ SNAKE_CASE
+          unless basename.split('.').all? { |fragment| fragment =~ SNAKE_CASE }
             add_offense(nil,
                         source_range(processed_source.buffer,
                                      processed_source[0..0],
diff --git a/spec/rubocop/cop/style/file_name_spec.rb b/spec/rubocop/cop/style/file_name_spec.rb
index b7096a1ac7c6..405b56620518 100644
--- a/spec/rubocop/cop/style/file_name_spec.rb
+++ b/spec/rubocop/cop/style/file_name_spec.rb
@@ -6,67 +6,79 @@
   subject(:cop) { described_class.new(config) }
 
   let(:config) do
-    Rubocop::Config.new({ 'AllCops' => { 'Includes' => includes } },
-                        '/some/.rubocop.yml')
+    Rubocop::Config.new(
+      { 'AllCops' => { 'Includes' => includes } },
+      '/some/.rubocop.yml'
+    )
   end
 
   let(:includes) { [] }
+  let(:source) { ['print 1'] }
+  let(:processed_source) { parse_source(source) }
 
-  it 'reports offense for camelCase file names ending in .rb' do
-    source = ['print 1']
-    processed_source = parse_source(source)
+  before do
     allow(processed_source.buffer)
-      .to receive(:name).and_return('/some/dir/testCase.rb')
+    .to receive(:name).and_return(filename)
     _investigate(cop, processed_source)
-    expect(cop.offenses.size).to eq(1)
   end
 
-  it 'reports offense for camelCase file names without file extension' do
-    source = ['print 1']
-    processed_source = parse_source(source)
-    allow(processed_source.buffer)
-      .to receive(:name).and_return('/some/dir/testCase')
-    _investigate(cop, processed_source)
-    expect(cop.offenses.size).to eq(1)
+  context 'with camelCase file names ending in .rb' do
+    let(:filename) { '/some/dir/testCase.rb' }
+
+    it 'reports an offense' do
+      expect(cop.offenses.size).to eq(1)
+    end
   end
 
-  it 'accepts offense for snake_case file names ending in .rb' do
-    source = ['print 1']
-    processed_source = parse_source(source)
-    allow(processed_source.buffer)
-      .to receive(:name).and_return('/some/dir/test_case.rb')
-    _investigate(cop, processed_source)
-    expect(cop.offenses).to be_empty
+  context 'with camelCase file names without file extension' do
+    let(:filename) { '/some/dir/testCase' }
+
+    it 'reports an offense' do
+      expect(cop.offenses.size).to eq(1)
+    end
   end
 
-  it 'accepts offense for snake_case file names without file extension' do
-    source = ['print 1']
-    processed_source = parse_source(source)
-    allow(processed_source.buffer)
-      .to receive(:name).and_return('/some/dir/test_case')
-    _investigate(cop, processed_source)
-    expect(cop.offenses).to be_empty
+  context 'with snake_case file names ending in .rb' do
+    let(:filename) { '/some/dir/test_case.rb' }
+
+    it 'reports an offense' do
+      expect(cop.offenses).to be_empty
+    end
   end
 
-  it 'accepts offense for snake_case file names with non-rb extension' do
-    source = ['print 1']
-    processed_source = parse_source(source)
-    allow(processed_source.buffer)
-      .to receive(:name).and_return('/some/dir/some_task.rake')
-    _investigate(cop, processed_source)
-    expect(cop.offenses).to be_empty
+  context 'with snake_case file names without file extension' do
+    let(:filename) { '/some/dir/test_case' }
+
+    it 'does not report an offense' do
+      expect(cop.offenses).to be_empty
+    end
+  end
+
+  context 'with snake_case file names with non-rb extension' do
+    let(:filename) { '/some/dir/some_task.rake' }
+
+    it 'does not report an offense' do
+      expect(cop.offenses).to be_empty
+    end
+  end
+
+  context 'with snake_case file names with multiple extensions' do
+    let(:filename) { 'some/dir/some_view.html.slim_spec.rb' }
+
+    it 'does not report an offense' do
+      expect(cop.offenses).to be_empty
+    end
   end
 
   context 'when the file is specified in AllCops/Includes' do
     let(:includes) { ['**/Gemfile'] }
 
-    it 'accepts the file name even if it is not snake_case' do
-      source = ['print 1']
-      processed_source = parse_source(source)
-      allow(processed_source.buffer)
-        .to receive(:name).and_return('/some/dir/Gemfile')
-      _investigate(cop, processed_source)
-      expect(cop.offenses).to be_empty
+    context 'with a non-snake_case file name' do
+      let(:filename) { '/some/dir/Gemfile' }
+
+      it 'does not report an offense' do
+        expect(cop.offenses).to be_empty
+      end
     end
   end
 end