Medical image segmentation is a key component in computer-aided diagnostic technology. In the past few years, the U-shaped architecture-based hierarchical model has become the mainstream approach, which however often fails to provide accurate results due to the loss of detailed features. To address this issue, this paper proposes a hierarchical ascending densely connected network, called HADCNet, to capture both local short-range and global long-range pathological features in a hierarchically organized network for more accurate segmentation. First, HADCNet devises a cross-scale ascending densely connected structure with a multi-path attention gate (MAG) to achieve full-scale interaction of global pathological features. Then, spatial-channel reconstruction units (called SRU and CRU) are introduced to decrease redundant computation and facilitate representative feature learning. Finally, multi-scale outputs are aggregated for final imaging. Extensive experiments demonstrate that our method achieves an average DSC of 84.45% and HD95 of 17.55 mm on the Synapse dataset (for multi-organ segmentation), with a similarly impressive performance on the ACDC (for cardiac diagnosis) and ISIC2018 datasets (for lesion segmentation). Additionally, HADCNet can be flexibly incorporated into existing backbone networks for better performance, e.g., combining HADC with TransUnet and SwinUnet, respectively, leads to 3.28% and 2.53% Dice score improvements.