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This paper focuses on path-inclusion secure two-party computation problem, and an efficient protocol for securely computing the path-inclusion problem is proposed. This problem is defined in the two parties setting, where Alice and Bob both have a path. The goal of Bob is to learn whether his path is included by the path Alice holds, without revealing it to Alice or learning anything else about Alice's path. Our construction is based on an automata evaluation sub-protocol. In our protocol, each path is coded into a string which reserves all information about the original path. Then both parties are involved in the automata evaluation sub-protocol. Finally one of them can learn whether one path includes the other one.