This paper proposes a novel cogging torque mitigation method for modular permanent magnet (PM) machines with flux gaps in alternate stator teeth. The slot openings of the modular PM machines are divided into two groups in a special way. By shifting the slot openings of two groups in opposite directions with the same angle, the machine cogging torque can be significantly reduced. Analytical formula of the desired shift angle is derived, and can be applicable to other modular machines with different slot/pole number combinations. Meanwhile, the influence of the proposed method on phase back-EMF is investigated and the three phase back-EMF waveforms remain balanced for all slot/pole number combinations after slot shifting. Experiments based on existing prototypes are carried out to validate the finite element modelling.