The series-winding permanent-magnet synchronous motor (SW-PMSM) has the merits of high output power and excellent control performance, as does the open-winding permanent-magnet synchronous motor (OW-PMSM). Meanwhile, it can greatly reduce the number of power devices. However, due to the existence of the zero-sequence path, zero-sequence current occurs, which can cause additional losses and torque ripples. Thus, this paper proposes a novel direct torque-control strategy for the SW-PMSM with zero-sequence current suppression capability (ZSCS-DTC). First, the series-winding topology (SWT) and the voltage vector distribution in the SW-PMSM drives are analyzed. Secondly, the basic DTC (B-DTC) scheme for the SW-PMSM is investigated, and the defects of zero-sequence current open-loop control in the B-DTC scheme are revealed. Thirdly, a new voltage vector synthesis scheme is proposed for suppression of zero-sequence current while ensuring bus voltage utilization. A switching table is reconstructed with the newly synthesized voltage vectors. On this basis, a ZSCS-DTC scheme for the SW-PMSM is proposed based on zero-sequence current closed-loop control so that electromagnetic torque, stator flux linkage and zero-sequence current can be controlled simultaneously. Finally, the effectiveness of the proposed ZSCS-DTC scheme for the SW-PMSM drives is verified.