This paper presents a long short-term memory (LSTM)-based ensemble learning framework for time-dependent reliability analysis. To deal with the time-dependent uncertainties, a LSTM network is first adopted to capture the system dynamics. As a result, time-dependent system responses for random realizations of stochastic processes can be accurately predicted by the LSTM. With realizations of the random variables and stochastic processes, multiple LSTMs are trained for generating a set of augmented data. Then a deep feedforward neural network (DFN) is employed to ensemble the knowledge extracted from LSTMs and generate a deep surrogate for the original time-dependent system responses. To improve the performance of DFN in terms of accuracy, the Gaussian process modeling technique is utilized for architecture design, where the number of neurons in the hidden layer is determined by minimizing the validation loss. With the DFN, the time-dependent system reliability can be directly approximated by using the Monte Carlo simulation. Two case studies are introduced to demonstrate the efficiency and accuracy of the proposed approach.