In recent years, salient object detection (SOD) in RGB-depth (RGB-D) images has attracted considerable research interest. We present a boundary-enhanced attention-aware network (BANet) for RGB-D SOD by combining boundary and saliency detection networks. In particular, depth maps were used to detect the saliency boundaries effectively, and the corresponding RGB images were used to predict the salient objects. Considering that the data contained in depth maps are insufficient, HSV images were employed as complements to enhance the boundary detection performances. Subsequently, an attention module was used to adaptively weigh the features from the RGB branch and boundary network to improve the SOD performance of the proposed BANet. A loss function combining saliency supervision, background supervision, and boundary supervision was designed to optimize the parameters of the BANet. Extensive experiments were conducted to assess the robustness and effectiveness of the proposed BANet. The results suggest that the proposed BANet shows a significant improvement over other representative SOD approaches.