Permanent magnet synchronous motor (PMSM) has been widely used in industry due to the advantages of high efficiency,high power density and high reliability. In this paper,a finite-control-set model-free predictive current control (FCS-MFPCC) based on extended control set is proposed for permanent magnet synchronous motor drives. At first,the mathematical model of PMSM is analyzed and the principle of finite-control-set model predictive current control (FCS-MPCC) is elaborated. Then,the traditional FCS-MFPCC based on linear extended state observer (LESO) is introduced. In order to tackle the issue of dissatisfactory steady-state performance of the traditional FCS-MFPCC,a control-set extension method based on the discrete space vector modulation (DSVM) is utilized,by which,the number of voltage vectors can be increased to 25. Following this,a fast optimization strategy is proposed to solve the problem of high computation burden caused by the extended control set. The principle and procedure of implementation of the strategy is explained in detail. Finally,the effectiveness and superiority of the proposed control strategy are verified by comparing the traditional and the proposed FCS-MFPCC methods based on a 500 W PMSM experimental test rig. The results show that the proposed control strategy can significantly enhance the steady-state performance of the system. The total harmonic distortion of stator current can be reduced from 10.07% to 6.48%.