How to efficiently utilize vast amounts of easily accessed aerial imageries is a critical challenge for researchers with the proliferation of high-resolution remote sensing sensors and platforms. Recently, the rapid development of deep neural networks (DNN) has been a focus in remote sensing, and the networks have achieved remarkable progress in image classification and segmentation tasks. However, the current DNN models inevitably lose the local cues during the downsampling operation. Additionally, even with skip connections, the upsampling methods cannot properly recover the structural information, such as the edge intersections, parallelism, and symmetry. In this paper, we propose the Web-Net, which is a nested network architecture with hierarchical dense connections, to handle these issues. We design the Ultra-Hierarchical Sampling (UHS) block to absorb and fuse the inter-level feature maps to propagate the feature maps among different levels. The position-wise downsampling/upsampling methods in the UHS iteratively change the shape of the inputs while preserving the number of their parameters, so that the low-level local cues and high-level semantic cues are properly preserved. We verify the effectiveness of the proposed Web-Net in the Inria Aerial Dataset and WHU Dataset. The results of the proposed Web-Net achieve an overall accuracy of 96.97% and an IoU (Intersection over Union) of 80.10% on the Inria Aerial Dataset, which surpasses the state-of-the-art SegNet 1.8% and 9.96%, respectively; the results on the WHU Dataset also support the effectiveness of the proposed Web-Net. Additionally, benefitting from the nested network architecture and the UHS block, the extracted buildings on the prediction maps are obviously sharper and more accurately identified, and even the building areas that are covered by shadows can also be correctly extracted. The verified results indicate that the proposed Web-Net is both effective and efficient for building extraction from high-resolution remote sensing images.