It is important to observe and study cancer cells' cycle progression in order to better understand drug effects on cancer cells. Time-lapse microscopy imaging serves as an important method to measure the cycle progression of individual cells in a large population. Since manual analysis is unreasonably time consuming for the large volumes of time-lapse image data, automated image analysis is proposed. Existing approaches dealing with time-lapse image data are rather limited and often give inaccurate analysis results, especially in segmenting and tracking individual cells in a cell population. In this paper, we present a new approach to segment and track cell nuclei in time-lapse fluorescence image sequence. First, we propose a novel marker-controlled watershed based on mathematical morphology, which can effectively segment clustered cells with less oversegmentation. To further segment undersegmented cells or to merge oversegmented cells, context information among neighboring frames is employed, which is proved to be an effective strategy. Then, we design a tracking method based on modified mean shift algorithm, in which several kernels with adaptive scale, shape, and direction are designed. Finally, we combine mean-shift and Kalman filter to achieve a more robust cell nuclei tracking method than existing ones. Experimental results show that our method can obtain 98.8% segmentation accuracy, 97.4% cell division tracking accuracy, and 97.6% cell tracking accuracy