In the general relativity theory gravitational energy-momentum density is usually described by a pseudo-tensor with strange transformation properties so that one does not have localization of gravitational energy. It is proposed to set up a gravitational energy-momentum density tensor having a unique form in a given coordinate system by making use of a bimetric formalism. Two versions are considered: (1) a bimetric theory with a flat-space background metric which retains the physics of the general relativity theory and (2) one with (...) a background corresponding to a space of constant curvature which introduces modifications into general relativity under certain conditions. The gravitational energy density in the case of the Schwarzschild solution is obtained. (shrink)