I find it very difficult to choose just one author who I would say is my favourite contemporary author, as it would depend if you were classing an "author" as just a writer of novels...
Personally, I value and enjoy short stories as much as novels, and so for that reason I would probably say Miranda July, who wrote one of my favourite books, No one belongs here more than you, which is a collection of short stories.
However, she hasn't yet published a novel, so taking this into account, I would say Ali Smith is my favourite contemporary author. She has written a brilliant collection of short stories, The First Person, and her latest novel, How To Be Both was shortlisted for the 2014 Man Booker Prize.
She has a unique way of writing which, I find, is unlike any other other author around today.