For reliability analysis of implicit limit state function, an improved line sampling method is presented on the basis of sample simulation in failure region. In the presented method, Markov Chain is employed to simulate the samples located at failure region, and the important direction of line sampling is obtained from these simulated samples. Simultaneously, the simulated samples can be used as the samples for line sampling to evaluate the failure probability. Since the Markov Chain samples are recycled for both determination of the important direction and calculation of the failure probability, the computational cost of the line sampling is reduced greatly. The practical application in reliability analysis for low cycle fatigue life of an aeronautical engine turbine disc structure under 0-takeoff-0 cycle load shows that the presented method is rational and feasible.