Abstract Trust prediction, aiming to predict the trust relations between users in a social network, is a key to helping users discover the reliable information. Many trust prediction methods are proposed based on the low-rank assumption of a trust network. However, one typical property of the trust network is that the trust relations follow the power-law distribution, i.e., few users are trusted by many other users, while most tail users have few trustors. Due to these tail users, the fundamental low-rank assumption made by existing methods is seriously violated and becomes unrealistic. In this paper, we propose a simple yet effective method to address the problem of the violated low-rank assumption. Instead of discovering the low-rank component of the trust network alone, we learn a sparse component of the trust network to describe the tail users simultaneously. With both of the learned low-rank and sparse components, the trust relations in the whole network can be better captured. Moreover, the transitive closure structure of the trust relations is also integrated into our model. We then derive an effective iterative algorithm to infer the parameters of our model, along with the proof of correctness. Extensive experimental results on real-world trust networks demonstrate the superior performance of our proposed method over the state-of-the-arts.