Add specs. Adjust filter.

app/models/project.rb

@@ -273,7 +273,7 @@ class Project < ActiveRecord::Base
     end
 
     def search_by_visibility(level)
-      where(visibility_level: visibility_levels[level.capitalize])
+      where(visibility_level: Gitlab::VisibilityLevel.const_get(level.upcase))
     end
 
     def search_by_title(query)

spec/requests/api/projects_spec.rb

@@ -90,6 +90,29 @@ describe API::API, api: true  do
         end
       end
 
+      context 'and using the visibility filter' do
+        it 'should filter based on private visibility param' do
+          get api('/projects', user), { visibility: 'private' }
+          expect(response.status).to eq(200)
+          expect(json_response).to be_an Array
+          expect(json_response.length).to eq(user.namespace.projects.where(visibility_level: Gitlab::VisibilityLevel::PRIVATE).count)
+        end
+
+        it 'should filter based on internal visibility param' do
+          get api('/projects', user), { visibility: 'internal' }
+          expect(response.status).to eq(200)
+          expect(json_response).to be_an Array
+          expect(json_response.length).to eq(user.namespace.projects.where(visibility_level: Gitlab::VisibilityLevel::INTERNAL).count)
+        end
+
+        it 'should filter based on public visibility param' do
+          get api('/projects', user), { visibility: 'public' }
+          expect(response.status).to eq(200)
+          expect(json_response).to be_an Array
+          expect(json_response.length).to eq(user.namespace.projects.where(visibility_level: Gitlab::VisibilityLevel::PUBLIC).count)
+        end
+      end
+
       context 'and using sorting' do
         before do
           project2