The aim to improve deficiency of current research on components retrieval is based on behavior specification matching, a multi-level component behavior matching model based on finite automata, which is presented in this paper. The study uses finite automata to model the behavior of components, refers to the idea of graph matching in graph theory, proposes six kinds of behavior matching relationships: equivalence behavior matching, extended behavior matching, compatible behavior matching, contain behavior matching, weak contain behavior matching and weak compatible behavior matching, analysis the implication relationships among these behavior matching relationships, and gives corresponding decision algorithms and adaptation methods of each behavior matching relationship. Based on these algorithms, a universal decision algorithm is proposed to reduce the complexity of subsequent component adapter and assembly. The matching model proposed in this paper provides a favorable technical support for components retrieval, based on behavior specification matching.