The matrix converter is a new generation of power electronic converters and is an alternative to back-to-back converters in applications that dimensions and weight are important. In this paper, a simple control algorithm for a three-phase asynchronous motor based on a direct torque control technique, which is fed through a three-phase direct matrix converter, is presented. For direct matrix converters, 27 switching modes are possible, which using the predictive control technique and for the different modes of the matrix converter, the motor behavior is estimated at the next sampling interval. Then the objective function is determined and the optimal possible mode is selected. Finally, the best switching mode is applied to the direct matrix converter. In order to evaluate the proposed method, simulation of the system in Matlab/Simulink software environment is performed. The results show the effectiveness of the proposed method.