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Proteins are usually grouped into complexes to perform functional tasks in organisms. So discovery of protein complexes is critical to understand principles of cellular organization and function. Recently high-throughput techniques have produced large amount of protein-protein interaction (PPI) data, which make it possible to detect protein complexes automatically from PPI data by using computational method. In this paper, we propose a local cluster detection algorithm (LCDA) to find the protein complexes. Super to other methods existed, LCDA is able to find both non-overlapping and overlapping clusters. The experiment results show that LCDA can detect protein complexes with very high accuracies.