With the increasing number of electric vehicles (EVs), a large amount of charging load will affect the safety and economic operation of the distribution network (DN). In this paper, an optimization dispatching strategy for integrated electricity and natural gas systems (IEGS) with fast charging stations (FCSs) is proposed to address the impact of fast charging loads. Firstly, the FCS load model is established based on the simulation of vehicle traveling and vehicle charging. Secondly, a natural gas supply model is established, which includes constraints such as the adjustment range, direction, and total number of supply flow adjustments. Then, an optimization dispatching strategy for IEGS based on energy storage and gas storage is proposed. Finally, the effectiveness of the proposed strategy is verified. The simulation results show that when the proposed strategy is applied, the voltage of FCS node will be stabilized within a good range. And the energy purchase cost will be reduced by more than 50%. The proposed method improves the carrying capacity of DN for FCSs.