Compared to the conventional doubly-salient reluctance motor (DRM) drives, the novel flux modulated DRM (FMDRM) drives can achieve a better overall torque performance due to the dc-biased sinusoidal current excitation. However, previous investigations only focus on the dc-biased and fundamental current components, and the contributions of current harmonics to the torque production are not clear. This article proposes an analytical torque ripple reduction strategy for open-winding FMDRM drives based on zero-sequence current (ZSC) harmonic regulation. First, the contribution of third-order ZSC harmonic to the electromagnetic torque is investigated together with the dc-biased sinusoidal current components. Second, an alternative torque component cancellation method is put forward, where the additional third-order ZSC is utilized to counteract the dominating part of the alternative torque generated by the dc-biased sinusoidal current for torque ripple reduction. Both the amplitude and initial phase angle of the additional third-order ZSC are calculated by the analytical equation of electromagnetic torque. Moreover, the corresponding three-dimensional current distribution is investigated to achieve the desired ZSC regulation. With the proposed scheme, the torque ripple can be effectively suppressed while maintaining high output torque capability and efficiency. Furthermore, experimental results are presented on a three-phase FMDRM prototype to verify the proposed strategy.