[Purposes] The load effects and structural resistances during the service period of engineering structures are uncertain and time-variant. Therefore, it is necessary to evaluate their safety through the time-variant reliability theory. Since the existing time-variant reliability methods have problems with accuracy and efficiency in highly nonlinear structures, this paper proposes a structural time-variant reliability analysis method based on Ring simulation and Markov chain Monte Carlo. [Methods] RS-MCMC introduces the Gauss-Legendre quadrature method to solve the time integration problem in time-variant reliability and transforms the time-variant reliability into a time-invariant reliability problem at a few time points for solution. A stepwise calculation scheme is proposed to adaptively adjust the range of the important domain, and the Markov chain Monte Carlo method is introduced to generate samples within the important domain. Finally, the time-variant reliability is estimated using the samples within the important domain, and the time-variant reliability of three typical cases is evaluated. [Findings] The evaluation results show that this method exhibits significant advantages in complex problems involving high nonlinearity and has the optimal comprehensive performance, with good accuracy, efficiency, and robustness. [Conclusions] RS-MCMC enriches the time-variant reliability analysis methods and provides new ideas for the innovative research of time-variant reliability analysis methods with its unique stepwise calculation scheme. Compared with the existing time-variant reliability analysis methods, RS-MCMC shows more superior comprehensive performance in solving complex time-variant reliability problems.