Accurately segmented nuclei are important, not only for cancer classification, but also for predicting treatment effectiveness and other biomedical applications. However, the diversity of cell types, various external factors, and illumination conditions make nucleus segmentation a challenging task. In this work, we present a new deep learning-based method for cell nucleus segmentation. The proposed convolutional blur attention (CBA) network consists of downsampling and upsampling procedures. A blur attention module and a blur pooling operation are used to retain the feature salience and avoid noise generation in the downsampling procedure. A pyramid blur pooling (PBP) module is proposed to capture the multi-scale information in the upsampling procedure. The superiority of the proposed method has been compared with a few prior segmentation models, namely U-Net, ENet, SegNet, LinkNet, and Mask RCNN on the 2018 Data Science Bowl (DSB) challenge dataset and the multi-organ nucleus segmentation (MoNuSeg) at MICCAI 2018. The Dice similarity coefficient and some evaluation matrices, such as F1 score, recall, precision, and average Jaccard index (AJI) were used to evaluate the segmentation efficiency of these models. Overall, the proposal method in this paper has the best performance, the AJI indicator on the DSB dataset and MoNuSeg is 0.8429, 0.7985, respectively.