The air-gap magnetic field analysis of the field-modulation double-stator electrical excitation synchronous machine (FM-DSEESM) is complicated due to its double stator and modulation-ring rotor configuration. Aimed to investigate the influence of the each part of the machine on the magnetic fields in the air-gaps, this study focuses on the permeance function analysis of FM-DSEESM to reveal its air-gap magnetic field distribution. Due to the limited physical space, the non-ferromagnetic segments of modulation-ring rotor in FM-DSEESM cannot be regarded as infinitely deep slots. Therefore, by adding a new flux line in the non-ferromagnetic segments, a new permeance function is proposed based on the calculation of the equivalent air-gaps. Then, analytical results of flux densities in the air-gaps are calculated and verified by finite element analysis. Finally, a FM-DSEESM prototype is fabricated to prove the feasibility of the permeance functions.