Nuclei segmentation occupies an important position in medical image analysis, which helps to predict and diagnose diseases. With the further research of deep learning, the task of nuclei segmentation has been automated. However, most existing methods require a great deal of manually marked full masks for training, which is time-consuming and labor-intensive, and can only be done by professional personnel. For the purpose of reducing the cost of labeling, we propose a weakly supervised method using generative adversarial training for segmentation of nucleus. In the case of no boundary, but only the centroid of the nucleus, the proposed method segmented the nucleus region with blurred boundaries. We first use the generative adversarial network(GAN) to generate the likelihood map of the nuclear centroid, then use Guided Backpropagation to visualize the pixels that contributes to the detection of the centroid of each nucleus, and finally obtain the segmentation mask of the nucleus by graph-cut. In addition, for the purpose of training the network better, we performed stain normalization on each pathological image. We have verified the proposed method on a multi-organ nuclei dataset. The final experiment results show that our advanced method achieves better segmentation performance than other weakly supervised methods, and can even reach the level of full supervision.