I have three suggestions for you. One of the most famous Canadian contemporary authors is Alice Munro, who writes short stories that are truly excellent. I have included a link below to more information about her, but you might want to check out some of her collections of short stories and see if you like them. She is generally recognised as being one of the best contemporary writers of short stories in the world, and not just in Canada. I personally have read The View from Castle Rock, which is the story of Munro's own ancestors and how they came to Canada and their lives their when they arrived. Other collections that are highly recommended are Too Much Happiness and Runaway.
The second suggestion is Green Grass, Running Water by Thomas King. This novel is another contemporary Canadian classic concerning the tension between indigenous culture and modern day values. It concerns the identity of a nation that in many ways is struggling to reconcile the rights and identity of first peoples with the new incomers that have swamped the country.
Lastly, from my perspective, the most famous Canadian author is Margaret Atwood whose works are truly stunning. She has written a large number of books, but to start off with try The Handmaid's Tale, which is a novel studied by many Grade 12 students in High School, that presents us with a terrifying vision of what the future of North America could look like.