The dynamic performance optimization of magnetic gear devices is essential to their industrialization. In this study, upon considering the magnetic field coupling characteristics of different components of a field modulated magnetic gear with intersecting axes (FMMGIA), we first obtained the magnetic coupling stiffnesses of these components via the finite element method. On this basis, we further established a dynamic model as well as the corresponding differential equations for the magnetic gear. Thereafter, we analyzed the modal characteristics and the influences of the primary design parameters on the modal frequency of the FMMGIA system. The results indicated that the magnetic coupling stiffnesses among the FMMGIA components were significantly lower than the meshing stiffnesses of the mechanical gears. In addition, the magnetic gear system consisted of three orders of torsional modals as well as three orders of horizontal vibration modals, among which the torsional modal frequencies of both the input and output rotors were substantially lower than others. Finally, parameters such as the minimum axial length and the permanent magnet remanence demonstrated considerable have impacts on the modal frequencies of the FMMGIA system.