Surface-mounted permanent magnet (SPM) motors with shaped magnets and a quasi-regular polygon rotor core (QPRC) are challenging to analyze in terms of accuracy and speed because of the special structure. This article proposes a new technique for the subdomain method which can accurately predict the electromagnetic performance of this kind of motor. The proposed new technique deals with the shaped magnet based on the method of magnet symmetrical segmentation, and it can solve the magnetic field generated by a pair of symmetrical segments together at each time. Especially, for the QPRC, the idea of variable rotor core radius is used in the new technique to analyze different segments. Furthermore, the new technique adopts a periodic boundary condition, which can quickly predict the electromagnetic performance of the motor, such as air-gap flux density, cogging torque, no-load back-EMF, winding inductance, electromagnetic torque and unbalanced magnetic force (UMF). This proposed new technique is applied to a 12-pole/3-phase SPM motor with shaped magnets and a QPRC, and its correctness is verified by finite-element analysis and experiment. The new technique can analyze the motor accurately, and its calculation speed is two orders of magnitude faster than that of the finite-element method.