[Objective] Circumferential staggered switched reluctance motor (SRM) utilizes auxiliary winding to compensate for torque drop in the main winding during commutation, which is of positive significance in suppressing the inherent torque ripple problem of SRM. Sector division is a critical factor affecting the efficacy of direct instantaneous torque control (DITC). [Methods] Firstly, the torque ripple suppression effect as well as the switching losses were considered comprehensively, and the turn-on and turn-off angles of the auxiliary winding were optimized by parametric methods. Then, a twelve-sector DITC strategy was developed by introducing the main winding advance conduction mechanism. Finally, a field-circuit coupled co-simulation model of circumferential staggered SRM was established to compare the operating performance between the nine-sector DITC strategy and twelve-sector DITC strategy with optimized turn-on and turn-off angles. [Results] The simulation results showed that compared with the nine-sector DITC strategy, the twelve-sector DITC strategy with optimized turn-on and turn-off angles significantly reduced the torque ripple coefficient by about 84%, and the torque per ampere also improved considerably by about 54%. Moreover, the main winding current of the demagnetized phase exhibited no current spike at the end of commutation, thereby alleviating its torque output burden during commutation and ensuring smoother current and torque transitions throughout the process. [Conclusion] The proposed twelve-sector DITC strategy effectively reduces the torque ripple during the commutation process of circumferential staggered SRM and enhances the torque per ampere and the system operating efficiency. It significantly enhances the smoothness of current profiles in the commutation region and the steady-state performance of the motor.