The kriging model has been used in the time-dependent reliability analysis which can have a good balance between efficiency and accuracy. To further improve the efficiency, the adjoint gradient-enhanced kriging (GEK) model is proposed with the reason that GEK model has better fitting performance. The gradient information is estimated by the adjoint method. The computational cost of obtaining the gradient of one data is equivalent to solving one origin physical model and one adjoint equation. That makes the gradient estimation independent of the problem dimension. Different strategies for gradient estimation of monotonic and non-monotonic performance functions are derived in the paper. The proposed method involves the same adaptive learning procedure as the active learning reliability method combining kriging and Monte Carlo simulation (AK-MSC). Then the failure probability is calculated by the Monte Carlo simulation with the low-computational cost GEK model. The major benefit is that the proposed method can achieve an accurate result with the small group of training data. Several demonstrated examples are used to show the good efficiency and accuracy of the proposed method.