In the case of discrete time control for multi-input multi-output systems, if the speed of each output response differs greatly from the others, it is better to use different sampling periods with each input-output system in order to improve the robustness of the controlled system and decrease computational load. This report suggests a 2-input 2-output generalized predictive control method with multirate sampling periods. First, the description of the plant is considered. Next, the predicted future output of the each output is expressed using the multistep predictor; the cost function is then modified, and the control law is determined. The simulation result shows that our proposed method is superior to the single-rate-sampling-period method in terms of computational load, response between sampling periods, and the ease of decision of design parameters.