With the wide application of microgrids in island area, the reliability evaluation of microgrid system becomes more complex and difficult. Firstly, k-means clustering algorithm is utilized for collecting typical scenes of microgrid operation with big data, and the "supply-load" characteristic which reflects the time correlation is used as the key feature. Secondly, a scenario probability distribution based Latin hypercube sampling method is proposed to ensure that the sampling frequency is identical to the scenario occurrence probability. Finally, according to the random sampling from the state time series of each component under different scenarios, the synthesis reliability index of each scenario can be computed by using the full probability formula. A microgrid benchmark is used to validate the effectiveness and accuracy of the proposed method. The results show that the proposed method proposed can quickly and correctly evaluate the reliability of the microgrid.