In this work, we propose a dual-network integrated logistic matrix factorization (DNILMF) algorithm to predict potential drug-target interactions (DTI). The prediction procedure consists of four steps: (1) inferring new drug/target profiles and constructing profile kernel matrix; (2) diffusing drug profile kernel matrix with drug structure kernel matrix; (3) diffusing target profile kernel matrix with target sequence kernel matrix; and (4) building DNILMF model and smoothing new drug/target predictions based on their neighbors. We compare our algorithm with the state-of-the-art method based on the benchmark dataset. Results indicate that the DNILMF algorithm outperforms the previously reported approaches in terms of AUPR (area under precision-recall curve) and AUC (area under curve of receiver operating characteristic) based on the 5 trials of 10-fold cross-validation. We conclude that the performance improvement depends on not only the proposed objective function, but also the used nonlinear diffusion technique which is important but under studied in the DTI prediction field. In addition, we also compile a new DTI dataset for increasing the diversity of currently available benchmark datasets. The top prediction results for the new dataset are confirmed by experimental studies or supported by other computational research.