Current surrogate modeling methods for time-dependent reliability analysis implement a double-loop procedure, with the computation of extreme value response in the outer loop and optimization in the inner loop. The computational effort of the double-loop procedure is quite high even though improvements have been made to improve the efficiency of the inner loop. This paper proposes a single-loop Kriging (SILK) surrogate modeling method for time-dependent reliability analysis. The optimization loop used in current methods is completely removed in the proposed method. A single surrogate model is built for the purpose of time-dependent reliability assessment. Training points of random variables and over time are generated at the same level instead of at two separate levels. The surrogate model is refined adaptively based on a learning function modified from time-independent reliability analysis and a newly developed convergence criterion. Strategies for building the surrogate model are investigated for problems with and without stochastic processes. Results of three numerical examples show that the proposed single-loop procedure significantly increases the efficiency of time-dependent reliability analysis without sacrificing the accuracy.