The critical execution paths play an important role in software system in terms of reducing the numbers of test date, detecting the vulnerabilities of software structure and analyzing software reliability. However, there are no e±cient methods to discover them so far. Thus in this paper, a complex network-based software algorithm is put forward to¯nd critical execution paths (FCEP) in software execution network. First, by analyzing the number of sources and sinks in FCEP, software execution network is divided into AOE subgraphs, and meanwhile, a Software Execution Network Serialization (SENS) approach is designed to generate execution path set in each AOE subgraph, which not only reduces ring structure's in°uence on path generation, but also guarantees the nodes' integrity in network. Second, according to a novel path similarity metric, similarity matrix is created to calculate the similarity among sets of path sequences. Third, an e±cient method is taken to cluster paths through similarity matrices, and the maximum-length path in each cluster is extracted as the critical execution path. At last, a set of critical execution paths is derived. The experimental results show that the FCEP algorithm is e±cient in mining critical execution path under software complex network.