Under the increasingly severe global energy situation, the traditional single power system energy structure has been unable to meet the needs of development. With the rapid development of power-to-gas(P2G) and gas turbine technology, the connection between the power system and natural gas system becomes closer. As the basis and key of coupling analysis of the power-gas system, the study of energy flow calculation is ofgreat importance. Firstly, the mathematical models of power system and natural gas system are analyzed. Aiming at the problem of choosing initial pressure value in natural gas system which is difficult to be solved in Newton method, the particle swarm optimization(PSO) is proposed to optimize the initial pressure value, and then Newton method is used to solve the energy flow of the power-gas integrated energy system(IES). Finally, the feasibility and accuracy of the proposed method are verified in the power-gas coupling system composed of IEEE 14-bus power distribution system and 14-node natural gas system.