I have a view controller in my app that has a navigation bar dragged on it in the storyboard. It was working fine in the iOS 6 but in iOS 7 it look like this:
you can simply do this:
1) add a constrain between the Navigation Bar and Top Layout Guide (select navigationBar, hold ctrl key and go to Bottom Layout Guide, unhold ctrl key)
2) select vertical spacing:

3) set constant to 0:

Result:

UPDATE
In your AppDelegate file you can add this:
func application(application: UIApplication, didFinishLaunchingWithOptions launchOptions: [NSObject: AnyObject]?) -> Bool
{
// Prevent Navigationbar to cover the view
UINavigationBar.appearance().translucent = false
}