This article proposes a novel analytical model which combines subdomain method and magnet equivalent circuit (MEC) method to predict the cogging torque of surface-mounted permanent magnet (SPM) motors with rotor eccentricity and magnet defects in any slot-pole combination cases. Firstly, the general solution of open-circuit magnetic field distribution in a slotless SPM motor with magnet defects is derived. Then, the motor is divided into several subdomains along the air-gap circumferential direction to consider the non-uniform air-gap caused by rotor eccentricity, where the air-gap lengths of each subdomain are considered to be uniform. Finally, the methods of conformal mapping and MEC combined with equivalent current is used to consider the effect of slotting and saturation, which is beneficial to improve the calculation precision. The magnetic field distributions and cogging torque calculated by the proposed model are consistent with the results of finite element analysis (FEA). Compared with the FEA, the proposed model can perform fast calculations of air-gap flux density and cogging torque under rotor eccentricity and magnet defects for SPM motors, which can be utilized for optimizing the motor towards fault tolerance.