In this paper, we propose a frequency bandwidth allocation method for satellite communications (SATCOM) based on the Model Predictive Control (MPC) and a sparse optimization method. To utilize limited frequency bandwidth resources of SATCOM efficiently, control strategies for SATCOM system are studied. We treat the frequency bandwidth allocation problem for SATCOM as an optimal control problem. Then, based on the assumption that a time variation model of communication requests is obtained, we propose an optimal control method based on the MPC and the sparse optimization. By utilizing the proposed method, the limited frequency bandwidth is utilized efficiently. We verify the effectiveness of the proposed method in a numerical simulation by using actual data of aircraft.