Abstract: Controlling double tearing modes instability by radio frequency (RF) wave current drive was explored by using numerical simulation with incompressible magnetohydrodynamics (MHD) in a periodic cylinder. The results show that a localized driven current along the background current direction on rational surfaces in Tokamak device has a suppression effect on the 3/1 double tearing modes instability, and the optimal initial localized driven current is current with I_cd=4%I and δ_cd=0.07a. In addition, only when the localized driven current is injected before the fast growth stage, the double tearing modes can be suppressed.