Community is an important attribute of information networks. Community search, as an important content of information network analysis, aims to find a set of nodes that meet the conditions specified by the user. As heterogeneous information networks contain more comprehensive and richer structural and semantic information, community search in such networks has received extensive attention in recent years. However, the existing community search methods for heterogeneous information networks cannot be directly applied when the search conditions are complex. For this reason, this study defines community search under complex conditions and proposes search algorithms considering asymmetric meta-paths, constrained meta-paths, and prohibited node constraints. These three algorithms respectively use the meta-path completion strategy, the strategy of adjusting batch search with labeling, and the way of dividing complex search conditions to search communities. Moreover, two optimization algorithms respectively based on the pruning strategy and the approximate strategy are designed to improve the efficiency of the search algorithm with prohibited node constraints. A large number of experiments are performed on real datasets, and the experimental results verify the effectiveness and efficiency of the proposed algorithms.