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In the research of nutation magnetic drive, the torque density of gears is an important index to evaluate its performance. Thus, the analysis and optimization of the magnetic torque is particularly important. A radial meshing nutation magnetic gear is presented and its operating principle is analyzed. Based on the magnetic vector potential theory of the constant magnetic field, the magnetic induction intensity model of the radial meshing nutation magnetic gears is established, and the mathematical model of the torque of the radial meshing magnetic gear is deduced. The genetic algorithm is used to optimize the structural parameters of the nutation magnetic gear, and the effectiveness of the optimization results is verified. The results show that the torque density after the optimization can be improved under the condition by limiting the size of magnetic gears and the amount of the magnetic pole material.