Although existing monocular depth estimation methods have made great progress, predicting an accurate absolute depth map from a single image is still challenging due to the limited modeling capacity of networks and the scale ambiguity issue. In this paper, we introduce a fully Visual Attention-based Depth (VADepth) network, where spatial attention and channel attention are applied to all stages. By continuously extracting the dependencies of features along the spatial and channel dimensions over a long distance, VADepth network can effectively preserve important details and suppress interfering features to better perceive the scene structure for more accurate depth estimates. In addition, we utilize geometric priors to form scale constraints for scale-aware model training. Specifically, we construct a novel scale-aware loss using the distance between the camera and a plane fitted by the ground points corresponding to the pixels of the rectangular area in the bottom middle of the image. Experimental results on the KITTI dataset show that this architecture achieves the state-of-the-art performance and our method can directly output absolute depth without post-processing. Moreover, our experiments on the SeasonDepth dataset also demonstrate the robustness of our model to multiple unseen environments.