This paper proposes a finite control set model predictive torque control (FCS-MPTC) with reduced computation burden for permanent magnet synchronous motor (PMSM). Based on discrete space vector modulation (DSVM), the proposed DSVM-MPTC extends the control set. Therefore, compared to the traditional FCS-MPTC, it greatly reduces the torque ripples and current harmonics while maintaining a constant switching frequency. Furthermore, a new voltage vector optimization strategy is employed to decrease the number of candidate voltage vectors from 38 to 13, the proposed DSVM-MPTC significantly reduces the computation burden without compromising the control performance. The validity of the proposed DSVM-MPTC is verified by comparative experiments.