Considering the coupling operation of power and natural gas systems in a power gas integrated energy system, this paper proposes a two-stage recovery strategy and recovery model using power storage, gas storage, P2G and other equipment. In the emergency recovery stage, to minimize the economic loss of the power gas integrated energy system in the recovery process, priority should be given to the restoration of load energy supply and part of the fault equipment, and the remaining fault equipment should be restored in the comprehensive recovery stage. A mixed integer model of two-stage fault recovery considering multiple devices is constructed, and the piecewise linearization method is used to deal with it. The optimal topology recovery sequence in the process of fault recovery is obtained, and the optimal recovery scheme is given. Finally, the comprehensive economic loss of the system in the recovery process is minimized and the recovery efficiency is maximized. Finally, the simulation results verify the effectiveness of the proposed strategy. This work is supported by the National Natural Science Foundation of China (No. 61873225).