When the permanent magnet synchronous motor (PMSM) was used as the driving device of the oil drilling rig system, the predictive control strategy of the PMSM in the oil drilling rig system based on feedforward compensation was proposed in view of the control requirements of fast response and strong robustness and the external disturbance in complex conditions. In this method, the predictive control based on the motor mathematical model was applied to the motor speed loop to realize the fast response and improve the robustness of the PMSM, and the extended state observer was introduced to realize the disturbance feedforward compensation. The simulation results showed that, compared with the speed PI control and dynamic matrix control of PMSM, the new control method had faster response and less overshoot, and the speed under the load interference exhibited less fluctuation and could be more quickly restored to the stable value.