Identifying protein complexes from protein interaction networks is an important task in the post-genomic era. With the development of high-throughput sequencing technology, the acquisition of protein interaction network data is becoming more and more convenient. The current protein complex recognition algorithms cannot well balance the hierarchical and overlapping properties of protein networks. In order to overcome these limitations, this paper proposes a Graph Wavelet based Protein Complex Discovery algorithm, GW-PCD. The method exploits the clustering analysis of protein interaction networks to find a modular mechanism by characterizing the distance between graph wavelet coefficients of protein pairs. Comparative experimental results show that GW-PCD enhances the performance of identifying protein complexes, which will provide valuable clues for further exploration of the unknown functions of proteins at the multiscale perspective.