The low-order high-amplitude component of axial electromagnetic force is the leading cause of electromagnetic vibration and noise of axial flux permanent magnet (AFPM) motors. In this paper, based on the analytical calculation of the axial electromagnetic force for a 20-pole 24-slot AFPM motor, the low-order axial electromagnetic force component is weakened by optimizing the motor’s electromagnetic structure. First, the three-dimensional (3-D) structural model of the motor is equated to a two-dimensional (2-D) analytical model, which is used to calculate the magnetic field generated by each of the armature winding and permanent magnet. Then, combined with the Maxwell tensor method, the axial electromagnetic force waveform is further obtained, and the target low-order high-amplitude component is extracted by 2-D Fourier analysis. Finally, taking this axial electromagnetic force component minimization as the target function of optimization, considering the output torque and ripple as constraints, the genetic algorithm is used to search for the optimal point by varying the structural parameters of the motor. The results show that the target low-order high-amplitude component of the axial electromagnetic force of the optimized motor is effectively suppressed, and the output torque ripple decreases with slightly increased torque amplitude, which provides a practical method for vibration and noise reduction of AFPM motors.