A number of studies has focused on the community detection in complex networks in recent years. Single-objective approaches which have only one optimization function (e. g., modularity or modularity density) may have weaknesses such as just a single community structure can be obtained or resolution limit. In this paper, a spectral clustering-based adaptive hybrid multi-objective harmony search algorithm (SCAH-MOHSA) combined with a local search strategy is proposed to detect the community structure in complex networks. At first, an improved spectral method is employed to convert the community detection problem into a data clustering issue while the length of the representation of a harmony in the harmony memory can be determined. Then, an adaptive hybrid multi-objective harmony search algorithm is used to solve the multi-objective optimization problem so as to resolve the community structure. The experiments on both synthetic and real world networks demonstrate our method achieves partition results which fit the real situation in an even better fashion.