As a typical flexible and adjustable resource, air conditioning load needs to take into account multiple constraints such as user comfort, policy norms and market income when participating in peak shaving of power grid. Therefore, the regulation preference and differential compensation mechanism are introduced, and a multi-objective optimization decision-making method for peak shaving of air conditioning cluster considering the sensitivity of user regulation is proposed. Firstly, an air conditioning cluster load model is constructed, which integrates the characteristics of regulation sensitivity and the equivalent thermal parameter model. Secondly, the peak-shaving framework of air-conditioning cluster with both simulation accuracy and regulation time is built: a differential compensation mechanism considering temperature regulation range and regulation time is established in the economic dimension, and a quantitative representation method of user satisfaction based on S-function is proposed in the user behavior dimension; Finally, in order to maximize the economic benefits of the aggregator and maximize the customer satisfaction, an optimal decision-making model of air-conditioning cluster peak shaving considering the regulation sensitivity is established, which is solved by combining Pareto frontier solution and knee-point decision-making method. The simulation results show that the proposed method can significantly improve the profit of peak adjustment of aggregators and realize the reasonable distribution of user-side subsidies on the premise of ensuring user comfort.