Adverse drug-drug interactions (DDIs) remain a leading cause of morbidity and mortality around the world. Identifying potential DDIs during the drug design process is critical in guiding targeted clinical drug safety testing. Although detection of adverse DDIs is conducted during Phase IV clinical trials, there are still a large number of new DDIs founded by accidents after the drugs were put on market. With the arrival of big data era, more and more pharmaceutical research and development data are becoming available, which provides an invaluable resource for digging insights that can potentially be leveraged in early prediction of DDIs. Many computational approaches have been proposed in recent years for DDI prediction. However, most of them focused on binary prediction (with or without DDI), despite the fact that each DDI is associated with a different type. Predicting the actual DDI type will help us better understand the DDI mechanism and identify proper ways to prevent it. In this paper, we formulate the DDI type prediction problem as a multitask dyadic regression problem, where the prediction of each specific DDI type is treated as a task. Compared with conventional matrix completion approaches which can only impute the missing entries in the DDI matrix, our approach can directly regress those dyadic relationships (DDIs) and thus can be extend to new drugs more easily. We developed an effective proximal gradient method to solve the problem. Evaluation on real world datasets is presented to demonstrate the effectiveness of the proposed approach.