We suggest a Lorentz-covariant theory of gravity that is equivalent to general relativity in weak gravitational field. We first derive the mass variation of a body falling freely in static gravitational field based on the principle of equivalence and the mass-energy relation. We then modify the standards of space-time in local gravitational field to keep them consistent with the standards in inertial frame of reference at infinity based on the influence of gravitational field on the light. The metric thus obtained agrees with Schwarzschild metric at first order approximation. The gravitational vector potential produced by a moving gravitational source can be obtained by applying Lorentz transformations in local gravitational field. Although inertial and non-inertial frames are equally valid in describing the motion of bodies in gravitational field, we still regard inertial frame, i.e. center of mass of the system, as the preferred frame of reference. This is because Newton's laws of motion only hold for inertial frames. The apsidal motion of binary system and the expansion of the universe can be explained more reasonably when observed from their respective centers of mass than that from relative motions. The expression of static metric in our theory does not contain gravitational radius, thus black hole and singularity do not exist. In our theory, the gravity in the presence of matter is the same as that in the vacuum, i.e. TOV equation does not hold. The maximum mass of a neutron star is about five times of solar mass based on our computation.