The concept of the gravitational field energy-momentum tensor is an interesting problem from the time of Einstein's general relativity established. It allures a lot of the theoretical and experimental physicsts to discuss and dispute it. The thesis is presented in a self-contained manner. We gives a review of the some topics about the gravitational theory including the preliminary of the spin 2 graviton and the canonical and metric energy-momentum tensors of the diverse fields. We derive the Yang-Mills gauge theory of the first-order and second-order formalisms by requiring minimal-coupling and gauge invariant. The Einstein gravitational theory in the first-order form is derived from the the linear theory, but for the second-order form we need to do infinite times of iterations. Finally, different definitons of the graviton energy-momentum tensor density is considered. We show that they are not equal since we can choose an inertial coordinate frame to eliminant the effect of gravity by the equivalence principle. Consequently, the local energy-momentum tensor is meaningless.