Aiming at the mechanical system related to multi-component failure, a reliability evaluation method of multi-component system based on time-varying Copula function was proposed. Firstly, the nonlinear Wiener process was introduced to characterize the performance degradation process, and the Copula function was used to characterize the correlation between multiple component failures. Secondly, based on the evolutionary equation of the Copula function approximation of the Fourier series, the fitting effects of the Fourier series on common time-varying forms were verified by Monte Carlo (MC) simulation. In addition, the likelihood ratio statistic was used to test the existence of time-varying correlation, indicating the necessity of time-varying correlation research. The example analysis shows that compared with the static correlation model, the time-varying correlation model has the log-likelihood function value increased by 4.36%, and the Akaike Information Criterion (AIC) decreased by 3.81%, achieving more accurate reliability evaluation results.