Separating overlapped nuclei is a major challenge in histopathology image analysis. Recently published approaches have achieved promising overall performance on public datasets; however, their performance in segmenting overlapped nuclei are limited. To address the issue, we propose the bending loss regularized network for nuclei segmentation. The proposed bending loss defines high penalties to contour points with large curvatures, and applies small penalties to contour points with small curvature. Minimizing the bending loss can avoid generating contours that encompass multiple nuclei. The proposed approach is validated on the MoNuSeg dataset using five quantitative metrics. It outperforms six state-of-the-art approaches on the following metrics: Aggregate Jaccard Index, Dice, Recognition Quality, and Pan-optic Quality.