To solve the two-sided matching problem with bounded rationality, we propose a decision-making method based on double reference points. Firstly, according to the theory of prospect and social comparison, we use the critical value given by each agent to set up personal reference point and social reference point, calculate the gain and loss of the ordinal value relative to the double reference points, and get the comprehensive benefit of each agent. Then, considering the different risk attitude of each agent to gain and loss based on the prospect theory, the comprehensive benefit of the agent is further transformed into the perceived value that depicts the satisfaction of the agent. On this basis, an optimization model aiming at maximizing the satisfaction of two-side agents is established, and the optimal matching solution can be obtained by solving this model. Finally, an example is given to illustrate the application of the method. Compared with the existing methods, the proposed method takes into account the influence of the individual dimension and the social dimension on the psychological behavior of the agent, and can reflect the actual perceived value and the bounded rationality characteristics of the agent more comprehensively and flexibly.