Nuclei segmentation is one of the important tasks for whole slide image analysis in digital pathology. With the drastic advance of deep learning, recent deep networks have demonstrated successful performance of the nuclei segmentation task. However, a major bottleneck to achieving good performance is the cost for annotation. A large network requires a large number of segmentation masks, and this annotation task is given to pathologists, not the public. In this paper, we propose a weakly supervised nuclei segmentation method, which requires only point annotations for training. This method can scale to large training set as marking a point of a nucleus is much cheaper than the fine segmentation mask. To this end, we introduce a novel auxiliary network, called PseudoEdgeNet, which guides the segmentation network to recognize nuclei edges even without edge annotations. We evaluate our method with two public datasets, and the results demonstrate that the method consistently outperforms other weakly supervised methods.