Given the increasing demand for natural gas, ensuring the safe operation of the system and the reliability of gas supply is a primary requirement. Existing facilities and regulation policies often fail to meet the demand during urban gas consumption peaks, causing certain impact on gas production and social life. The implementation of demand response measures can guide users to cut or shift energy use during peak demand periods, in order to reduce peak energy use, relieve system peaking pressure, reduce load-cutting demand and extend facilities expansion plans. Based on the price elasticity theory, this paper uses the K-means clustering algorithm to divide peak and valley periods, incorporates optimization methods, and establishes a multi-objective optimization model for demand response with minimum system peak-to-valley differences and maximum customer satisfaction. This is solved using the primal interior point method to develop a reasonable natural gas demand response plan. The Pareto optimal solution set is obtained by taking the natural gas demand of a certain day in Zhengzhou city as an example, and it can be seen that the implementation of natural gas demand response can balance the system demand and achieve the purpose of peak load shifting.