With the continuous development of integrated energy system and the deepening of the coupling relationship between multiple energy flows, the safe and stable operation of the system has received widespread attention. At present, the security of integrated energy system is mostly researched from the perspective of power grid and rarely researched from the perspective of equipment. This study proposes a day-ahead optimal dispatch method of integrated electric-heat-cool-gas energy system based on N-1 safety criterion, which ensures the normal operation of integrated energy system after the failure of a power supply equipment by increasing appropriate amount of power supply. In this study, the changes in equipment power and operating cost before and after equipment failure under the dispatch method considering N-1 safety criterion and the changes in equipment power and operating cost before and after equipment failure under the dispatch method without considering N-1 safety criterion are investigated by numerical simulation. The results show that when a power supply equipment fails, the average daily loss of load is 6139.99 kW for the dispatch method without considering the N-1 safety criterion and the average daily loss of load is 0 kW for the dispatch method considering the N-1 safety criterion. Therefore, the dispatch method considering the N-1 safety criterion performs better in terms of reliability. When a power supply equipment fails, the average operating cost is 5127.71 USD for the dispatch method without considering the N-1 safety criterion and the average operating cost is 4125.56 USD for the dispatch method considering the N-1 safety criterion. Therefore, the dispatch method considering the N-1 safety criterion performs better in terms of economy.