Abstract Stochastic block models (SBMs) provide a statistical way modeling network data, especially in representing clusters or community structures. However, most block models do not consider complex characteristics of networks such as scale-free feature, making them incapable of handling degree variation of vertices, which is ubiquitous in real networks. To address this issue, we introduce degree decay variables into SBM, termed power-law degree SBM (PLD-SBM), to model the varying probability of connections between node pairs. The scale-free feature is approximated by a power-law degree characteristic. Such a property allows PLDSBM to correct the distortion of degree distribution in SBM, and thus improves the performance of cluster prediction. Experiments on both simulated networks and two real-world networks including the Adolescent Health Data and the political blogs network demonstrate the validity of the motivation of PLD-SBM, and its practical superiority.