This paper proposes modelling and optimization of a new reluctance axial flux magnetic gear (RAMG) with stationary outer rotor and advantages of lower permanent magnet usage. Due to the less use of the PMs, this structure has a higher economic interest, more reliability, and very simple and robust structure than its conventional ones. Gear ratio and operating principles are extracted and verificated using 3-D finite element method (FEM) simulations. Finally, a parametric optimization is done based on effective dimensions in design procedure with maximum torque density objective function. The magnetic flux distributions of optimized RAMG are calculated by 3-D FEM, as well as static and dynamic magnetic torques are derived correspondingly.