Cervical cell segmentation plays an important role in intelligent cervical cancer diagnosis. However, the performance of current methods is still limited because cervical cells are overlapping, adhesion, and even visual inseparability. In addition, deep learning-based instance segmentation methods need large amounts of labeled data, leading to significant consumption of manpower and material resources. To solve these problems, we propose a multi-branch instance segmentation network for cervical cells, named MBSeg. This method selects cervical cell images and automatically annotates them at the pixel level using active learning. Next, we leverage CondInst, a one-stage instance segmentation network, and improve it by adding a new over-lapping segmentation branch. This branch generates overlapping mask maps, which are integrated into the original mask branch to enhance attention on the receptive fields of the overlapping areas. Furthermore, we employ a Nucleus Enhanced Module (NEM) to accurately locate nuclei and a Mask-Assisted Segmentation (MAS) module to minimize interference from impurities. Experiments on our dataset MS-cellSeg, the public Cx22, and ISBI2015 datasets demonstrate the superiority of our method in segmenting overlapping cervical cells.