Deeply analyzing the temporal characteristics of gas pipeline accidents is crucial to the safety management of gas pipeline. In this study, gas distribution pipeline accidents recorded from 1986 to 2020 provided by PHMSA have been chosen to explore the characteristics of gas pipeline failure frequency in the United States. The result indicates that the failure frequency of gas pipelines has been reduced with the improvement of safety management. The analysis results show that the gas pipeline accidents occurred in the U.S. from 1986 to 2020 are temporal connected. This is due to the fact that the leading failure causes are related with human factors, which have strong temporal correlations. Improving the pipeline safety management can reduce the temporal dependence. However, there are essential temporal pattern differences among gas pipeline accident sequences of different severity. Accurate prediction of the gas pipeline accident occurrence can improve the quantitative risk assessment of gas pipeline accidents, and also help the pipeline management personnel to develop an efficient emergency response plan. Therefore, as for the quantitative risk assessment of gas pipeline accidents, it is necessary to carry out in-depth analysis of the occurrence probability according to the severity of the accidents.