Performance analysis of a linear permanent magnet Vernier machine (LPMVM), which has a complex structure, is mostly based on the finite element methods, while for its optimisation or sensitivity analysis a quick mathematical technique is desirable. This paper introduces an LPMVM and its principles of operation. Then, a mixed subdomain and magnetic equivalent circuit are applied to extract magnetic field equations in various parts of the machine, in which the end-effect in included. Besides, the electromotive force, thrust force, normal force and electric equivalent circuit are determined. An LPMVM was prototyped and tested to verify the accuracy of the proposed method.