In recent years, using the discrete model of the object and considering the finite switching state characteristics of power electronic systems, finite control set model predictive control (FCS-MPC) has been widely used in synchronous reluctance motor (SynRM) drive system to promote the energy efficiency. However, the FCS-MPC modeling process heavily depends on the SynRM mathematical model, and the accuracy of motor parameters directly affects the control effect. To solve the above problems, a data-driven MPC (DD-MPC) method is proposed. This method does not need the SynRM mathematical model information. It only utilizes the input-output data relationship of the SynRM. So the “synchronization of modeling and control” is realized. In addition, in order to ensure the convergence and stability of DD-MPC system, a DD-MPC data relation with high update rate is designed. By analyzing the current change information corresponding to the recent three-voltage-vector output, the corresponding current change relation of the global voltage vectors is deduced and updated. Finally, the control effect of DD-MPC is tested and analyzed based on a 25 kW prototype. Compared with the traditional FCS-MPC, the proposed method can effectively improve the robustness and stability, while maintaining the rapidity and flexibility of FCS-MPC.