This paper presents an inner-type of magnetic gears for non-contact driving, based on the nutation gearing principle. An improved three-dimensional analytical model, based on the magnetic vector potential of rectangular permanent magnets, via the equivalent current, is deduced for the proposed nutation magnetic gears. The transformation of coordinates is applied for a global field solution. The analytical model and the finite element model have analyzed the output torque of the nutation magnetic drive, respectively. The results show that the values calculated by the two models are consistent. The proposed analytical model can provide a reference for the design and optimization of nutation magnetic gears and other permanent magnetic mechanisms with rectangular magnets.