@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。

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。

从示例应用程序中，可以看到这种变化。 https://github.com/mpospese/MPFoldTransition/

#pragma mark - UINavigationController(MPFoldTransition)

@implementation UINavigationController(MPFoldTransition)

//- (void)pushViewController:(UIViewController *)viewController animated:(BOOL)animated
- (void)pushViewController:(UIViewController *)viewController foldStyle:(MPFoldStyle)style
{
    [MPFoldTransition transitionFromViewController:[self visibleViewController] 
                                  toViewController:viewController 
                                          duration:[MPFoldTransition defaultDuration]  
                                             style:style 
                                        completion:^(BOOL finished) {
                                            [self pushViewController:viewController animated:NO];
                                        }
     ];
}

- (UIViewController *)popViewControllerWithFoldStyle:(MPFoldStyle)style
{
    UIViewController *toController = [[self viewControllers] objectAtIndex:[[self viewControllers] count] - 2];

    [MPFoldTransition transitionFromViewController:[self visibleViewController] 
                                  toViewController:toController 
                                          duration:[MPFoldTransition defaultDuration] 
                                             style:style
                                        completion:^(BOOL finished) {
                                            [self popViewControllerAnimated:NO];
                                        }
     ];

    return toController;
}

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];

虽然这里所有的答案都很棒，而且大多数工作得很好，但有一个稍微简单一点的方法可以达到同样的效果……

推动:

  NextViewController *nextViewController = [[NextViewController alloc] init];

  // Shift the view to take the status bar into account 
  CGRect frame = nextViewController.view.frame;
  frame.origin.y -= 20;
  frame.size.height += 20;
  nextViewController.view.frame = frame;

  [UIView transitionFromView:self.navigationController.topViewController.view toView:nextViewController.view duration:0.5 options:UIViewAnimationOptionTransitionFlipFromRight completion:^(BOOL finished) {
    [self.navigationController pushViewController:nextViewController animated:NO];
  }];

流行:

  int numViewControllers = self.navigationController.viewControllers.count;
  UIView *nextView = [[self.navigationController.viewControllers objectAtIndex:numViewControllers - 2] view];

  [UIView transitionFromView:self.navigationController.topViewController.view toView:nextView duration:0.5 options:UIViewAnimationOptionTransitionFlipFromLeft completion:^(BOOL finished) {
    [self.navigationController popViewControllerAnimated:NO];
  }];}

使用iJordan的答案作为灵感，为什么不简单地在UINavigationController上创建一个Category来在整个应用程序中使用，而不是复制/粘贴这个动画代码的所有地方?

UINavigationController + Animation.h

@interface UINavigationController (Animation)

- (void) pushViewControllerWithFlip:(UIViewController*) controller;

- (void) popViewControllerWithFlip;

@end

UINavigationController+Animation.m

@implementation UINavigationController (Animation)

- (void) pushViewControllerWithFlip:(UIViewController *) controller
{
    [UIView animateWithDuration:0.50
                     animations:^{
                         [UIView setAnimationCurve:UIViewAnimationCurveEaseInOut];
                         [self pushViewController:controller animated:NO];
                         [UIView setAnimationTransition:UIViewAnimationTransitionFlipFromRight forView:self.view cache:NO];
                     }];
}

- (void) popViewControllerWithFlip
{
    [UIView animateWithDuration:0.5
                     animations:^{
                         [UIView setAnimationCurve:UIViewAnimationCurveEaseInOut];
                         [UIView setAnimationTransition:UIViewAnimationTransitionFlipFromRight forView:self.view cache:NO];
                     }];

    [self popViewControllerAnimated:NO];
}

@end

然后简单地导入UINavigationController+Animation.h文件并正常调用它:

[self.navigationController pushViewControllerWithFlip:[[NewViewController alloc] init]];

[self.navigationController popViewControllerWithFlip];