Unless you use Typemock or Moles, you can’t.
In ASP.NET MVC you are not supposed to be using HttpContext.Current. Change your base class to use ControllerBase.ControllerContext – it has a HttpContext property that exposes the testable HttpContextBase class.
Here’s an example of how you can use Moq to set up a Mock HttpContextBase:
var httpCtxStub = new Mock<HttpContextBase>();
var controllerCtx = new ControllerContext();
controllerCtx.HttpContext = httpCtxStub.Object;
sut.ControllerContext = controllerCtx;
// Exercise and verify the sut
where sut
represents the System Under Test (SUT), i.e. the Controller you wish to test.