To avoid the huge time consumption in the initial and optimum design of modular linear permanent magnet vernier machine when finite element method (FEM) was used to calculate the flux leakage coefficient, the equivalent magnetic network model was established for the machine. During the modeling, the fringing effect in the airgap was taken into consideration, the equivalent permeances of the permanent magnet group and the stator teeth at different relative positions were calculated, and the mathematical analytical expressions of magnetic permeability and flux leakage coefficient of the machine at different relative positions in one cycle were obtained. Finally, the FEM method was used to verify the correctness and accuracy of the mathematical analytical expressions. The research results provided a theoretical basis for the design of modular linear permanent magnet vernier machines.