This paper proposes a finite control set model predictive current control (FCS-MPCC) with grey prediction for surface mounted PMSM drives. The basic FCS-MPCC is combined with grey prediction to improve the dynamic performance current control. Grey system takes into account both certain and uncertain information in real system, and use the rolling optimal grey sequence to predict the control current for cost function. The performance is demonstrated in both simulation and experiment. The results illustrate that FCS-MPCC with grey prediction expresses a good current response under the load disturbance and good performance under different parameter variations. Meanwhile the steady-state performance of current can be assured.