Nuclei segmentation models significantly improves the efficiency of nuclei analysis. However, existing models exhibit performance limitations, especially when adapting to unknown or untrained cell datasets. Improving the generalization ability of models remains a challenge. To address this issue, we introduce an edge enhanced two-stage network for nuclei segmentation. The first stage of the model focuses on extracting the edges of the nuclei. The second stage utilizes this edge information to focus on processing segmentation tasks. We designed an Edge Enhancement block that effectively fuses edge information and original images, alleviating the problem of blurred nuclei boundaries caused by uneven staining, thereby improving the segmentation accuracy of the model. Comprehensive evaluation shows that our model significantly improves the DICE, AJI, and PQ indices on the MoNuSeg public dataset. Experimental results on cross-dataset testing show that the proposed method outperforms the state-of-the-art nuclei segmentation methods.