•Proposed a fast reliability evaluation method for integrated power-gas system (IPGS).•Presented a novel consequence analysis model of IPGS failures based on graph theory.•Proposed a tailor-made importance sampling algorithm for IPGS reliability evaluation.•Reliability indices are developed in the aspects of system, customers and components. The supply reliability is a vital concern in the planning of integrated power-gas systems (IPGS). Previous reliability evaluation approaches of IPGS bring massive computational burdens due to the complex consequence (status) analysis model and numerous status samples in Monte Carlo simulation (MCS). In this paper, a systematic assessment approach is proposed to evaluate the supply reliability of IPGS rapidly. Firstly, a novel optimal load shedding model of IPGS is presented based on the stochastic capacity network model of gas system and the power flow model, which reduces the computational complexity of consequence analysis. Then, a tailor-made importance sampling (IS) method based on cross-entropy is proposed for IPGS to improve the efficiency of MCS. Through evaluating the criticality of training samples, the IS method accordingly alters the unavailability parameters of electricity and gas components, so that crucial risk events of IPGS are sampled more frequently in MCS. Furthermore, reliability indices of IPGS are developed in three hierarchies: system reliability, customer availability and component importance, which provide comprehensive references for system planners. Finally, numerical simulations are performed on two IPGS cases and the results validate the proposed approach significantly improves the computational efficiency of supply reliability evaluation for IPGS.