Existing community search methods are difficult to deal with the complex and diverse search requirements of users and difficult to integrate network structure and node attributes to measure the correlation between nodes in high-dimensional and sparse heterogeneous information networks (HINs). In order to solve the problems, the community search problem of mutual information maximization over HINs was proposed, the definition of community with mutual information maximization was given, and a corresponding community search method, community search with mutual information maximization (CSMIM) was designed. The user's search requirements were defined as query constraints, and a query constraint deep graph infomax (QC-DGI) model was proposed to learn node embedding by extracting the structure, semantics and node attribute information in HINs to effectively calculate the mutual information between nodes. Then, according to the given query information, the mutual information maximization criterion was used to search the target community. In addition, an optimization strategy based on user feedback was proposed to realize the personalized calculation of mutual information from global to local, so as to improve the accuracy of search results. Finally, extensive experiments on real HINs dataset were performed, and experimental results prove that the proposed method can effectively search the community of a given node according to the search requirements, and has higher accuracy than the representative baseline methods.