You can do it like this:

**In your main view controller:**

    func showModal() {
        let modalViewController = ModalViewController()
        modalViewController.modalPresentationStyle = .OverCurrentContext
        presentViewController(modalViewController, animated: true, completion: nil)
    }

**In your modal view controller:**

    class ModalViewController: UIViewController {
        override func viewDidLoad() {
            view.backgroundColor = UIColor.clearColor()
            view.opaque = false
        }
    }

**If you are working with a storyboard:** 

Just add a Storyboard Seque with `Kind` set to `Present Modally` to your modal view controller and on this view controller set the following values:

    Background = Clear Color
    Drawing = Uncheck the Opaque checkbox
    Presentation = Over Current Context


As [Crashalot][1] pointed out in his comment: Make sure the **segue** only uses `Default` for both `Presentation` and `Transition`. Using `Current Context` for `Presentation` makes the modal turn black instead of remaining transparent.


  [1]: http://stackoverflow.com/users/144088/crashalot
  
  [Source](http://stackoverflow.com/a/33106533/499052)