Clusters of nuclei are frequently observed in thick tissue section images. It is very important to segment overlapping nuclei in many biomedical applications. Many existing methods tend to produce under segmented results when there is a high overlap rate. In this paper, we present a curvature weighting based algorithm which weights each pixel using the curvature information of its nearby boundaries to extract markers, each of which represents an object, from input images. Then we use marker-controlled watershed to obtain the final segmentation. Test results using both synthetic and real cell images are presented in the paper.