记住，在Swift中，扩展绝对是你的朋友!

public extension UINavigationController {

    /**
     Pop current view controller to previous view controller.

     - parameter type:     transition animation type.
     - parameter duration: transition animation duration.
     */
    func pop(transitionType type: String = kCATransitionFade, duration: CFTimeInterval = 0.3) {
        self.addTransition(transitionType: type, duration: duration)
        self.popViewControllerAnimated(false)
    }

    /**
     Push a new view controller on the view controllers's stack.

     - parameter vc:       view controller to push.
     - parameter type:     transition animation type.
     - parameter duration: transition animation duration.
     */
    func push(viewController vc: UIViewController, transitionType type: String = kCATransitionFade, duration: CFTimeInterval = 0.3) {
        self.addTransition(transitionType: type, duration: duration)
        self.pushViewController(vc, animated: false)
    }

    private func addTransition(transitionType type: String = kCATransitionFade, duration: CFTimeInterval = 0.3) {
        let transition = CATransition()
        transition.duration = duration
        transition.timingFunction = CAMediaTimingFunction(name: kCAMediaTimingFunctionEaseInEaseOut)
        transition.type = type
        self.view.layer.addAnimation(transition, forKey: nil)
    }

}

基于jordanperry为swift 4更新的答案

用于推送UIViewController

let yourVC = self.storyboard?.instantiateViewController(withIdentifier: "yourViewController") as! yourViewController
    UIView.animate(withDuration: 0.75, animations: {() -> Void in
    UIView.setAnimationCurve(.easeInOut)
    self.navigationController?.pushViewController(terms, animated: true)
    UIView.setAnimationTransition(.flipFromRight, for: (self.navigationController?.view)!, cache: false)
})

为流行

UIView.animate(withDuration: 0.75, animations: {() -> Void in
    UIView.setAnimationCurve(.easeInOut)
    UIView.setAnimationTransition(.flipFromLeft, for: (self.navigationController?.view)!, cache: false)
})
navigationController?.popViewController(animated: false)

这就是我总是设法完成这项任务的方法。

推动:

MainView *nextView=[[MainView alloc] init];
[UIView  beginAnimations:nil context:NULL];
[UIView setAnimationCurve:UIViewAnimationCurveEaseInOut];
[UIView setAnimationDuration:0.75];
[self.navigationController pushViewController:nextView animated:NO];
[UIView setAnimationTransition:UIViewAnimationTransitionFlipFromRight forView:self.navigationController.view cache:NO];
[UIView commitAnimations];
[nextView release];

流行:

[UIView  beginAnimations:nil context:NULL];
[UIView setAnimationCurve:UIViewAnimationCurveEaseInOut];
[UIView setAnimationDuration:0.75];
[UIView setAnimationTransition:UIViewAnimationTransitionFlipFromLeft forView:self.navigationController.view cache:NO];
[UIView commitAnimations];

[UIView beginAnimations:nil context:NULL];
[UIView setAnimationDelay:0.375];
[self.navigationController popViewControllerAnimated:NO];
[UIView commitAnimations];

我还是从这里得到了很多反馈所以我将继续更新它，使用动画块这是苹果推荐的制作动画的方法。 推动:

MainView *nextView = [[MainView alloc] init];
[UIView animateWithDuration:0.75
                         animations:^{
                             [UIView setAnimationCurve:UIViewAnimationCurveEaseInOut];
                             [self.navigationController pushViewController:nextView animated:NO];
                             [UIView setAnimationTransition:UIViewAnimationTransitionFlipFromRight forView:self.navigationController.view cache:NO];
                         }];

流行:

[UIView animateWithDuration:0.75
                         animations:^{
                             [UIView setAnimationCurve:UIViewAnimationCurveEaseInOut];
                             [UIView setAnimationTransition:UIViewAnimationTransitionFlipFromLeft forView:self.navigationController.view cache:NO];
                         }];
[self.navigationController popViewControllerAnimated:NO];

我知道这个帖子很旧了，但我想我应该发表我的意见。你不需要制作一个自定义动画，有一个简单(可能是hack)的方法来做它。不使用push，而是创建一个新的导航控制器，使新的视图控制器成为那个nav控制器的根视图控制器，然后从原始的nav控制器中呈现出nav控制器。现在是很容易自定义的许多风格，不需要做一个自定义动画。

例如:

UIViewcontroller viewControllerYouWantToPush = UIViewController()
UINavigationController newNavController = UINavigationController(root: viewControllerYouWantToView)
newNavController.navBarHidden = YES;
self.navigationController.present(newNavController)

你可以随心所欲地改变演示风格。

@Magnus回答，只有Swift(2.0)才会这样

    let transition = CATransition()
    transition.duration = 0.5
    transition.timingFunction = CAMediaTimingFunction(name: kCAMediaTimingFunctionEaseInEaseOut)
    transition.type = kCATransitionPush
    transition.subtype = kCATransitionFromTop
    self.navigationController!.view.layer.addAnimation(transition, forKey: nil)
    let writeView : WriteViewController = self.storyboard?.instantiateViewControllerWithIdentifier("WriteView") as! WriteViewController
    self.navigationController?.pushViewController(writeView, animated: false)

旁注:

你也可以用Segue做这个，只需要在prepareForSegue或shouldPerformSegueWithIdentifier中实现。但是，这也会保留默认动画。要解决这个问题，你必须转到故事板，单击Segue，取消选中“Animates”框。但这将限制你的应用在IOS 9.0及以上(至少当我在Xcode 7中这样做时)。

在segue中，最后两行应该替换为:

self.navigationController?.popViewControllerAnimated(false)

即使我设为false，它还是会忽略它。

以下是我如何在Swift中做同样的事情:

推动:

    UIView.animateWithDuration(0.75, animations: { () -> Void in
        UIView.setAnimationCurve(UIViewAnimationCurve.EaseInOut)
        self.navigationController!.pushViewController(nextView, animated: false)
        UIView.setAnimationTransition(UIViewAnimationTransition.FlipFromRight, forView: self.navigationController!.view!, cache: false)
    })

流行:

实际上，我对上面的一些回答做了一些不同的处理——但由于我是Swift开发的新手，这可能是不对的。我重写了viewWillDisappear:animated:，并在那里添加了弹出代码:

    UIView.animateWithDuration(0.75, animations: { () -> Void in
        UIView.setAnimationCurve(UIViewAnimationCurve.EaseInOut)
        UIView.setAnimationTransition(UIViewAnimationTransition.FlipFromLeft, forView: self.navigationController!.view, cache: false)
    })

    super.viewWillDisappear(animated)