Searching for new methods to enhance stability of antiferromagnetic (AFM) skyrmion during its motion is an important issue for AFM spintronic devices. In this work, we numerically study the spin-polarized current-induced dynamics of a distorted AFM skyrmion based on the Landau-Lifshitz-Gilbert simulations of the model with an anisotropic Dzyaloshinskii-Moriya (DM) interaction. It is demonstrated that the DM interaction anisotropy induces the skyrmion deformation, which suppresses the distortion during the motion and enhances the stability of the skyrmion. Moreover, the effect of the DM interaction anisotropy on the skyrmion velocity is investigated in detail, and the simulated results are further explained by Thiele's theory. This work unveils a promising strategy to enhance the stability and the maximum velocity of AFM skyrmion, benefiting future spintronic applications.