The detection of building edges from very high resolution (VHR) remote sensing imagery is essential to various geo-related applications, including surveying and mapping, urban management, etc. Recently, the rapid development of deep convolutional neural networks (DCNNs) has achieved remarkable progress in edge detection; however, there has always been the problem of edge thickness due to the large receptive field of DCNNs. In this paper, we proposed a multi-scale erosion network (ME-Net) for building edge detection to crisp the building edge through two innovative approaches: (1) embedding an erosion module (EM) in the network to crisp the edge and (2) adding the Dice coefficient and local cross entropy of edge neighbors into the loss function to increase its sensitivity to the receptive field. In addition, a new metric, Ene, to measure the crispness of the predicted building edge was proposed. The experiment results show that ME-Net not only detects the clearest and crispest building edges, but also achieves the best OA of 98.75%, 95.00% and 95.51% on three building edge datasets, and exceeds other edge detection networks 3.17% and 0.44% at least in strict F1-score and Ene. In a word, the proposed ME-Net is an effective and practical approach for detecting crisp building edges from VHR remote sensing imagery.