Covariant Theory of Gravitation in the Spacetime with Finsler Structure

The theory of gravitation in the spacetime with Finsler structure is constructed. It is shown that the theory keeps general covariance. Such theory reduces to Einstein’s general relativity when the Finsler structure is Riemannian. Therefore, this covariant theory of gravitation is an elegant realization of Einstein’s thoughts on gravitation in the spacetime with Finsler structure.