The studies on drug-protein interactions (DPIs) had significant for drug repositioning, drug discovery, and clinical medicine. The biochemical experimentation (in vitro) requires a long time and high cost to be confirmed because it is difficult to estimate. Therefore, a feasible solution is to predict DPIs efficiently with computers. We propose a link prediction method based on drug-protein interaction (DPI) local structural similarity (DLS) for predicting the DPIs. The DLS method combines link prediction and binary network structure to predict DPIs. The ten-fold cross-validation method was applied in the experiment. After comparing the predictive capability of DLS with the improved similarity-based network prediction method, the results of DLS on the test set are significantly better. Moreover, several candidate proteins were predicted for three approved drugs, namely captopril, desferrioxamine and losartan, and these predictions are further validated by the literature. In addition, the combination of the Common Neighborhood (CN) method and the DLS method provides a new idea for the integrated application of the link prediction method.