Abstract: Non-circular gears are widely used because they combine the characteristics of gear and cam drives. To achieve different variable speed transmission characteristics, a Fourier non-circular gear with a pitch curve fitted according to the Fourier series equation is proposed in this paper. Firstly, a mathematical model is established based on the geometric relationship of the gear pair. To ensure the continuous transmission of the Fourier non-circular gear, the progressive and regressive method and the golden section method are combined to solve the center distance of the gear pair. To avoid undercutting during the generation of the tooth profile, a judgment formula for the non-concave pitch curve of the non-circular gear is derived. The single-factor research method is used to analyze the influence laws of various design parameters a_i,i\in \left0,n\right and b_i,i\in \left1,n\right on the pitch curve and transmission ratio of the non-circular gear, and the coupling response between parameters is analyzed using orthogonal experiments. Then, a virtual prototype simulation test is used for verification. It is found that the size of the gear depends on the parameter a_0 , and a_i and b_i affect the transmission characteristics of the gear. By adjusting various design parameters, Fourier non-circular gear mechanisms with different transmission characteristics can be obtained. The theoretical calculation and simulation results are basically consistent. The maximum error between the theoretical and simulation test results of the transmission ratio is \Delta i_12\max =0.134\;53 , and the root mean square error is \Delta _RMS=0.002\;9 , which shows the feasibility of the proposed design method and the correctness of the established mathematical model. The research results of this paper provide a theoretical basis for the application of Fourier non-circular gears to solve practical engineering problems.