It has been recognized that the magnetic reconnection process is of great importance in high-energy astrophysics. We develop a new two-dimensional relativistic resistive magnetohydrodynamic ((RMHD)-M-2) code and carry out numerical simulations of magnetic reconnection. We find that the outflow velocity reaches the Alfven velocity in the inflow region and that a higher Alfven velocity provides a higher reconnection rate. We also find that Lorentz contraction plays an important role in enhancement of the reconnection rate.