how to implement the authentication in Single Page Application?

As the title says,I want to build a App that run in browser with a Single Html page.but how to implement the Authentication.and my solution is:

  1. the server-side is all the RESTful APIs,which can used by multiple Platform,web ,mobile side ,etc.and every API that need auth will be get a token to parse,if the API does not get a token return 401.
  2. cuz my first practise is in the browser,so I need to request for the token to get login,and when the app needs to request the auth-APIs,I will put the token in the header for requesting...

and my questions is : does it safe enough? any other better solution?

No it's not safe enough if the token is accessible through javascript for the same reason that you should set your cookies to http only and restrict to ssl. If a hacker can inject javascript into your app, it can steal the token and use it from their machine.

For that reason I suggest you use a secure, http only cookie instead of the token when using a website.

If your API is going to be accessed from a native mobile app then you could add a token to each url.

Having a custom header in the http request might cause issues with certain proxies which might not pass all headers through. A cookie is nothing more than a standardised http header so you might as well reuse that.

What you could also consider using is OAuth if you're going to allow 3rd party apps access to parts of your API.

There is no reason why you could not use cookies for browser based clients and an ApiKey query parameter for other clients.