Abstract: Compared to traditional magnetic gears, the eccentric harmonic magnetic gear（EHMG） has larger output torque density with high transmission ration. The key in design and optimization to ensure excellent performances of the EHMG is that how to predict the internal magnetic field distribution accurately. In this paper, the fractional linear transformation combined with the ratio permeance function, obtains the analytical solution of EHMG air-gap magnetic fields. To overcome the tangential permeance of subduction faults, the polar coordinates of radial and tangential permeance calculations are transferred into Cartesian coordinates x, y direction permeance calculation. To Modify the non-eccentric the air gap magnetic field component, and then according to the principle of superposition, eccentric harmonic magnetic gear air-gap magnetic field distribution was synthesized. Results from this analytical method are consistent with corresponding finite element analysis, which proves the accuracy of the proposed analytical model.