This article shows a two-dimensional analysis model for predicting eddy current loss in a winding flux-switching permanent magnet under an open-circuit. The finite-element method is used for electrical machine design; however, this numerical method is always time consuming. Depending on the geometry, the mesh quality of the finite-element method should be high, and thus the finite-element method is more time consuming for special electrical machines. To solve this problem, a sub-domain model using Fourier analysis is improved for a flux-switching permanent magnet machine. It is obtained by solving Poisson and Laplace equations in polar coordinates for each domain, i.e., the magnet, air gap, rotor and stator slots, as well as external region. The model accounts for the influence of interaction between the stator slots and air gap, as well as rotor slots and air gap. Magnetic field distribution, flux linkage, back-electromotive force, cogging torque, and eddy current loss waveforms are derived from the analytical method and verified by finite-element analysis. To the best knowledge of the authors, such an analysis has not been carried out previously.