With the increasing of available protein-protein interaction (PPI) data, many computational methods have been explored to identify protein complexes from PPI networks. Majority of algorithms employ the feature of local neighbors to detect local dense subgraphs which correspond to protein complexes. Those approaches neglect the inherent core-attachment structure of protein complexes, which to an extent affect the protein complexes of prediction accuracy. In this paper, we propose a new algorithm for predicting protein complexes, deriving from the framework of the core-attachment. The proposed method first obtains the triangular structures of the core of protein complexes, name as cells, in which the edge-clustering coefficient is used. And then the cells are expanded to protein complex cores based on the closeness. Finally, the attachments are added to their corresponding cores to form the final protein complexes. The experimental results on two yeast PPI data show our method outperform the existing algorithms in terms of matched protein complexes and biological significance using two benchmark data sets.