Protein complexes are important entities to organize various biological systems. However, they are still limited in availability. Thus, it is a challenging problem to predict protein complexes computationally from existing genome-wide data sets, like protein-protein interaction (PPI) networks. In this paper, we propose an efficient algorithm for predicting protein complexes by random walking on a PPI network. The algorithm is designed based on the method of node-weighted expansion of a cluster, which simulates a random walk with restarts with the weighted nodes of the cluster. We have validated the biological significance of the results using curated complexes in the CYC2008 database. We have compared our method to a clustering-based method, MCL, and a repeated random walk-based method, RRW, and found that our algorithm outperforms the other algorithms.