The morphology of the nuclei represents most of the clinical pathological information, and nuclei segmentation is a vital step in current automated histopathological image analysis. Supervised machine learning-based segmentation models have already achieved outstanding performance with sufficiently precise human annotations. Nevertheless, outlining such labels on numerous nuclei is extremely professional needing and time consuming. Automatic nuclei segmentation with minimal manual interventions is highly needed to promote the effectiveness of clinical pathological researches. Semi-supervised learning greatly reduces the dependence on labeled samples while ensuring sufficient accuracy. In this paper, we propose a Multi-Edge Feature Fusion Attention Network (MEFFA-Net) with three feature inputs including image, pseudo-mask and edge, which enhances its learning ability by considering multiple features. Only a few labeled nuclei boundaries are used to train annotations on the remaining mostly unlabeled data. The MEFFA-Net creates more precise boundary masks for nucleus segmentation based on pseudo-masks, which greatly reduces the dependence on manual labeling. The MEFFA-Block focuses on the nuclei outline and selects features conducive to segment, making full use of the multiple features in segmentation. Experimental results on public multi-organ databases including MoNuSeg, CPM-17 and CoNSeP show that the proposed model has the mean IoU segmentation evaluations of 0.706, 0.751, and 0.722, respectively. The model also achieves better results than some cutting-edge methods while the labeling work is reduced to 1/8 of common supervised strategies. Our method provides a more efficient and accurate basis for nuclei segmentations and further quantifications in pathological researches.