Recent studies suggest that drug-drug interaction (DDI) prediction via computational approaches has significant importance for understanding the functions and co-prescriptions of multiple drugs. However, the existing silico DDI prediction methods either ignore the potential interactions among drug-drug pairs (DDPs), or fail to explicitly model and fuse the multi-scale drug feature representations for better prediction. In this study, we propose RGDA-DDI, a residual graph attention network (residual-GAT) and dual-attention based framework for drug-drug interaction prediction. A residual-GAT module is introduced to simultaneously learn multi-scale feature representations from drugs and DDPs. In addition, a dual-attention based feature fusion block is constructed to learn local joint interaction representations. A series of evaluation metrics demonstrate that the RGDA-DDI significantly improved DDI prediction performance on two public benchmark datasets, which provides a new insight into drug development.