Model-free predictive current control (MFPCC) has excellent parameter robustness owing to unused parameters of the controller. However, the method has the current gradient update stagnation problem due to the limited availability of only 7 voltage vectors, which results in a high current/torque ripple. To address this shortcoming, an enhanced MFPCC for permanent magnet synchronous machines (PMSMs) incorporating discrete space vector modulation (DSVM) is proposed in this paper. First, the basic voltage vectors are expanded from 7 to 37 by DSVM. Then, a novel current gradient updating method is developed to effectively reduce the current/torque ripple caused by current gradient updating stagnation. Finally, a candidate vector preselection method is designed to simplify the calculation process of current gradient updating. The effectiveness of the proposed method is verified on a 2 kW PMSM driving experimental platform. The experimental results show that the THD is reduced from 25.5% to 7.8% while the dq-axes current ripple is respectively reduced from 5.1 A and 5.8 A to 2.2A and 1.5 A.