There are the problems of limited working frequency range and serious output vibration waveform distortion of a tri-axial standard vibrator, which are affected by the low natural frequency and nonlinear characteristics of the leaf-spring decoupling structure. Firstly, the natural frequency and output waveform distortion characteristics of the tri-axial standard vibrator under corresponding changing parameters are obtained through ANSYS modal and transient dynamic analyses based on the determined key parameter simplified combinations of the decoupling structure. In further, a multi-element nonlinear regression method is used to establish the regression equations that can accurately represent the nonlinear changing relationships between the natural frequency, distortion degree and key structural parameters. A multi-parameter optimization of the leaf-spring decoupling structure is implemented based on the NSGAII genetic algorithm. The optimal leaf-spring structural parameters are obtained by increasing the first 3 natural frequencies and bending mode natural frequencies by 123. 95% and 166. 85% , respectively. The distortion is reduced by 36. 83% . Finally, the experimental test shows that the performance of the tri-axial standard vibrator corresponding to the optimal leaf-spring decoupling structure has been improved in both natural frequency and output waveform distortion, which evaluate the effectiveness of the multi-parameter optimization design of the leaf-spring decoupling structure based on the proposed genetic algorithm method. It provides a reference for the optimization design of other multi-dimensional flexible structures.