The permanent magnet assisted synchronous reluctance motor (PMA-SynRM) with the asymmetric rotor design can effectively improve the utilization of magnetic torque and reluctance torque, thus to improve the torque density. However, it also brings about problems of cogging torque and excessive torque ripple. In order to solve this problem of excessive torque ripple, the torque ripple is suppressed from two aspects of the motor structure and control methods. In terms of motor structure, opening the auxiliary slot and changing the pole and slot combinations with different winding methods. In control methods, the torque ripple is suppressed by analyzing the torque harmonic components and injecting the specified harmonic current. Then, with the aid of finite element method (FEM), the influence of three methods on the torque characteristics and performance of the PMA-SynRM with asymmetric rotor structure is analyzed. The results show that the three methods can effectively suppress the torque ripple, and the 27-slot stator with distributed windings structure can effectively suppress the cogging torque and torque ripple of this kind of motor under the premise of ensuring the full use of the torque component. This work can better enhance the flux focusing characteristics of the asymmetric rotor structure, laying a foundation for the application of the asymmetric rotor PMA-SynRM in more fields.