how to publish mvc application as native app.

First of all, you should have explained what you mean by "MVC". This can be understood as the well-known architectural pattern: http://en.wikipedia.org/wiki/Model_View_Presenter[^].

If you meant that, the question would not make any sense, because this architecture is unrelated to any particular platform, it could be native or not, anything.

But "MVC4" suggests that you mean ASP.NET framework based on this architectural pattern: http://www.asp.net/mvc[^].

In this case, the question makes even less sense. For ASP.NET applications, the concept "native" itself makes no sense. It has at least two parts: server side and client side. Server side is based on .NET; and the code works under CLR. It's not just "impossible" to make it native; it is something which makes no sense: if some "native" code existed, it's unclear what it would be; certainly not .NET and not ASP.NET and hence the code using "MVC4" framework. And the client-side code is executed in a browser, it would be ridiculous to discuss if it is "native" or not.

The whole question makes no sense because you, essentially, talk about nothing.

—SA