The axial-flux permanent magnet vernier machine (PMVM) is a competitive machine applied in the field of direct-drive which features on low speed and high torque. The rotor of axial-flux PMVM has a tendency to deflect to stator under the effect of the large and unbalanced axial electromagnetic force, which probably results in the collision between rotor and stator. Therefore, this article presents an analysis and optimization of the axial electromagnetic force of the axial-flux PMVM. First, the three-dimensional finite-element model (3-D FEM) is converted to equivalent two dimensional finite-element model (2-D FEM) for further axial electromagnetic force derivation and optimization. Subsequently, four design parameters that are sensitive to the axial electromagnetic force are selected and analyzed for further optimization, which aims to obtain an equal output torque, and reduce the axial electromagnetic force of entire rotor and peak force density of axial electromagnetic force as much as possible. Finally, a Kriging model between the objective functions and design parameters is constructed based on considerable simulation results, and genetic algorithm is applied to search for the proposed optimized result which is ultimately validated by simulation.