Drug-target interaction identification is an essential step of drug discovering and adverse effect prediction. In real bio-environment, the connections among drugs and targets, as well as themselves construct a complex heterogeneous network, and profoundly affect the predictive performance of drug-target interactions. However, the current methods usually focus on the drug-target interactions alone, which may be very sparse and with numerous noises, may not produce satisfactory prediction results. In this paper, we propose a novel approach, dual-graph regularized robust PCA in heterogeneous network, for drug-target interaction prediction task. In particular, we aim at decompose the bipartite graph of drug-target interactions into two low-rank matrices, which represent the latent representations of drugs and targets respectively, and smooth the drug-drug and target-target graphs simultaneously. Moreover, an improved robust PCA model is used to suppress the widespread noisy connections in the decomposition stage. For the optimization, we design an efficient algorithm to solve few subproblems with close-form solution. Finally the extensive experiments on real world drug-target heterogeneous networks are presented to show the effectiveness of the proposed methods.