This paper proposes the time-dependent reliability model of structures under different stochastic loads based on the stress–strength interference (SSI) model and probabilistic statistical theory. First, the different stochastic loads mean that the loads are discrete, and that one applied load is from random variable and the other applied load may be from another random variable, and the cumulative effect and correlation are considered when they are applied for multiple times. Second, two different time-dependent reliability models, with and without considering strength degradation, are established in this paper. Meanwhile, the relationship between the discrete load frequency and time is described using Poisson process, and the time-dependent reliability model under continuous time is also provided. Finally, the proposed time-dependent reliability model of structures is validated with the Monte Carlo simulation (MCS), and the effectiveness of the proposed method is testified.