Abstract: Multi-phase machines with back-EMF harmonics can be utilized to improve the torque density. However, back-EMF harmonics will induce additional torque ripples under post-fault operation. In this paper, a fault-tolerant control strategy for five-phase permanent magnet synchronous machines with non-sinusoidal back-EMF under open-circuit fault is proposed. Based on the torque equation under single-phase open-circuit fault, the general closed-form solution for disturbance-free operation is derived and the theoretical basis for suppressing torque pulsation with harmonic current is given. Therefore, the low-order harmonic currents are injected in the synchronous frame to suppress the torque pulsation caused by the 3^rd harmonic back-EMF. To obtain optimal solution, two operation modes are applied, such as minimum copper loss (ML) or maximum output torque (MT), to simultaneously optimize harmonic current coefficients. Compared with the existing method, the proposed method could produce the same copper loss under ML mode and effectively improve torque output capacity under MT mode. Finally, the experiment results for five-phase permanent magnet synchronous machines under postfault operation verify the accuracy and effectiveness.