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In real life, garbage has caused great pollution to the environment. A garbage classification system is an effective way to manage this issue, and is an innovation in Shanghai, China. Innovation diffusion is the topic of this paper. This study uses a mathematical statistics method to formulate individual bounded rationality, and uses the specific graph structure of a scale-free network to characterize group structure. Then, a model of group behavior is constructed and the simulation experiment is run on the Python platform. The results show that: (1) In the case of general cognitive ability and high value innovation, most individuals in the group will accept the innovation in the process of innovation dissemination in a garbage classification system after several rounds of the game; (2) it is more helpful to improve the cognitive ability of individuals and the true value of innovation for the diffusion of innovation; and (3) the larger a group, the greater the scope of innovation diffusion and the more time is needed. It is helpful to expand the scope and reduce the time of innovation diffusion by increasing connections among individuals. The innovation of this study is the characterization of individual bounded rationality, which has a certain theoretical value. Meanwhile, the research results of this paper have important practical significance for the promotion of garbage classification, which can be used to popularize the concept of garbage classification.