What are some good writers in English literature, whose native language is not English?

There are many writers who have influenced English literature and to name a few: Arthur Conan Doyle, George Bernard Shaw, Edwin Morgan, Adam Smith, Robert Louis Stevens, Samuel Beckett ...

I think the questions intends to start with "Who" but my list would include Arundhati Roy, Salman Rushdie, Tusiata Avia, Anita Desai, Bapsi Sidhwa and Rohinton Mistry. 

Strange quedtiob. Maybe, Salman Rushdie

Thanks for the invitation and agree with Professor Akhil Kumar

If you are beginning your journey into English literature, I would honestly recommend you to forget the classics, unless that is your main goal.

If you are seeking to improve your vocabulary, here are the books I would recommend:

- Sherlock Holmes by Sir Arthur Conan Doyle

- Harry Potter (I am serious as this is a splendid read and a great way to improve your language skills).

- The Alchemist and other books from Paolo Coelho

However, if you are indeed seeking books from classic literature, here are my recommendations:

- Animal Farm by George Orwell

- A Christmas Carol by Charles Dickens

- Frankenstein by Mary Shelley

- The Picture of Dorian Grey by Oscar Wilde

Hope this helps and good luck!