This paper presents unit commitment model for integrated electric and natural-gas systems considering two-way coupling of power-to-gas and gas turbine. Minimizing the sum of integrated energy systems operation costs becomes the objective function. The security transmission constraints of the natural-gas and electricity networks are considered simultaneously. Linearization method is adopted to get the linear model. The test case consists of the 6-node electric network, the 10-node gas network and the coupling elements. The nonlinear model and the linearized model are calculated respectively and their solving efficiency is compared. The two scenarios with or without power-to-gas on system operational states and cost are analyzed simultaneously. Test results show that the linear model improves the solving efficiency of the unit commitment of the integrated electric and natural-gas systems. And the power-to-gas could effectively improve the operation economy and reliability of integrated electric and natural-gas systems. This work is supported by National Natural Science Foundation of China (No. 51877071) and Science and Technology Project of State Grid Jiangsu Electric Power Company Ltd (No. J2019017).