Gas supply systems are generally not allowed to operate under leakage conditions; pipeline networks with extensive leakage after earthquakes must be shut down immediately for inspection and repair. However, under low seismic intensity or minor pipeline damage, complete shutdown is often impractical due to urban gas demand, and the system may operate under slight leakage conditions. To evaluate the reliability of gas supply networks under such conditions, this study integrates post-earthquake pipeline failure states with a leakage model for buried gas pipelines and establishes a hydraulic analysis model that accounts for leakage. A three-state failure probability model is coupled with Monte Carlo method to randomly generate post-earthquake pipeline failure states. The functional reliability of the gas supply network under specified seismic conditions is then evaluated using a “pressure-driven” hydraulic analysis method, and the service status of user nodes after the earthquake is quantified. Based on this framework, the functional reliability of a low-pressure gas supply network under different seismic intensities is analyzed through 1 000 Monte Carlo simulations. The case study results show that the system maintains high seismic reliability under VI and VII earthquakes, while reliability decreases significantly under VIII earthquakes. These findings provide a scientific basis for prost-earthquake reliability assessment and repair planning of urban gas supply pipeline networks.