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The interdependency of electric and natural gas systems is becoming stronger. The challenge of how to meet various energy demands in an integrated energy system (IES) with minimal cost has drawn considerable attention. The optimal scheduling of IESs is an ideal method to solve this problem. In this study, a day-ahead optimal scheduling model for IES that included an electrical system, a natural gas system, and an energy hub (EH), was established. The proposed EH contained detailed models of the fuel cell (FC) and power to gas (P2G) system. Considering that the optimal scheduling of an IES is a non-convex complex optimal problem, a piecewise self-adaptive particle swarm optimization (PCAPSO) algorithm based on multistage chaotic mapping was proposed to solve it. The objective was to minimize the operating cost of the IES. Three operation scenarios were designed to analyze the operation characteristics of the system under different coupling conditions. The simulation results showed that the PCAPSO algorithm improved the convergence rate and stability compared to the original PSO. An analysis of the results demonstrated the economics of an IES with the proposed EHs and the advantage of cooperation between the FC and P2G system.