This paper proposes a stress-strength time-varying correlation interference model for structural reliability analysis using Copulas. First, the stochastic stress is developed by incorporating the interaction between basic variables and time variable into the quadratic response surface method, and the stochastic strength is characterized by the linear or exponential degradation model. Second, the Copula selection method is given, and we propose time-varying stable (unstable) model for Kendall's tau to describe the time-varying correlation characteristic. Third, the structural reliability estimation method is developed, especially the method for the nondifferentiable Copulas can be used to calculate the probability in any area for any type of Copula when the marginal distribution is continuous. Finally, the lower confidence limit of structural reliability is given based on the survival coefficient. The comparison results of the high-temperature structural reliability estimation from different situations are illustrated in the simulation example to demonstrate the availability of the proposed model.