Accurate segmentation of cells and nuclei is the key technology in computer-assisted diagnosis of cervical cancer. In this paper, a multi-active contour method, which was based on semantic segmentation of the U-Net model, was proposed for overlapping cells segmentation. First, each sample image was labeled as three parts: background, cell and cell nucleus. Then, the U-Net model was trained to segment the cervical images to obtain the cell and cell nucleus; meanwhile, the cell clump information could be obtained. The active contour for each cell was initialized according to the distance from the pixel point to the cell nucleus, and the energy functional was established based on shape prior of cells, the edge prior of images and the mutual prior between different contours. Finally, every single cell was segmented by minimizing the proposed energy functional. Experiment comparisons show that the segmentation method proposed in this paper can segment cervical cells under complex conditions, including independent cells, overlapping cells and their nuclei. The experimental results also prove the effectiveness of proposed method.