The growing availability of scanned whole-slide images (WSIs) has allowed nephropathology to open new possibilities for medical decision-making over high-resolution images. Diagnosis of renal WSIs includes locating and identifying specific structures in the tissue. Considering the glomerulus as one of the first structures analyzed by pathologists, we propose here a novel convolutional neural network for glomerulus segmentation. Our end-to-end network, named DS-FNet, combines the strengths of semantic segmentation and semantic boundary detection networks via an attention-aware mechanism. Although we trained the proposed network on periodic acid-Schiff (PAS)-stained WSIs, we found that our network was capable to segment glomeruli on WSIs stained with different techniques, such as periodic acid-methenamine silver (PAMS), hematoxylin-eosin (HE), and Masson trichrome (TRI). To assess the performance of the proposed method, we used three public data sets: HuBMAP (available in a Kaggle competition), a subset of the NEPTUNE data set, and a novel challenging data set, called WSI_Fiocruz. We compared the DS-FNet with six other deep learning networks: original UNet, our attention version of U-Net called AU-Net, U-Net++, U-Net3Plus, ResU-Net, and DeepLabV3+. Results showed that DS-FNet achieved equivalent or superior results on all data sets: On the HuBMAP data set, it reached a dice score (DSC) of 95.05%, very close to the first place (95.15%); on the NEPTUNE and WSI_Fiocruz data sets, DS-FNet obtained the highest average DSC, whether on PAS-stained images or images stained with other techniques. To the best we know, this is the first work to show consistently high performance in a one-to-many-stain glomerulus segmentation following a thorough protocol on data sets from different medical labs.