Advantages of API testing are:

Test for core functionality: API testing provides access to the application without the user interface. The core functionality of the application will be tested before the GUI tests. This will help to detect the minor issue which can become bigger during the GUI testing.
Time effective: API testing is less time consuming than GUI testing. Particularly, API test requires less code so it can provide better and faster test coverage compare to GUI test automation. This will reduce the cost for the testing project.
Language Independent: In API testing data is exchange using XML or JSON. These transfer mode are completely language-independent, which allows users to select any code language when adopting automation test service for the project.
Easy Integration with GUI: API tests provide highly integrable tests which is useful to perform functional GUI tests after GUI tests. Simple integration would allow new user accounts to be created within the application before GUI started.