Abstract: An implicit Monte Carlo method was developed to solve the radiation hydrodynamics problems, which considered the special relativistic effects. The problem was solved in three steps by using an operator-splitting manner. The first step was to calculate the hydrodynamics equation without the radiation source term. The second step was to simulate the radiation transport equation using the implicit Monte Carlo method, and the deposited energy and momentum were tallied in the particle tracking progress. The relativistic effects in this progress were considered. Lastly the momentum and energy density were updated by the statistical results of the second step. Hydrodynamics process and the motion process of Monte Carlo particle were performed in the lab frame. However, the matter-radiation interaction is in the local commoving frame. Finally, numerical experiments were carried out on several typical problems in radiation hydrodynamics. The result verifies the applicability of the method and the correctness of the code.