In this paper, we propose and develop a novel saturation component based fuzzy Mumford-Shah model for color image segmentation. The main feature of this model is that we determine different segments by using the saturation component in hue, saturation, and value (HSV) color space instead of the original red, green and blue (RGB) color space. The proposed model is formulated for multiphase segmentation of color images with the assumption that a piecewise smooth function is approximated by the product of a piecewise constant function and a smooth function. The piecewise constant function and the smooth function are used to represent different segments and to estimate the bias field respectively in the color image. The approximation is calculated based on the saturation component which is particularly useful to distinguish edges and capture the inherent correlation among red, green and blue channels in color images. Experimental results are presented to demonstrate that the segmentation performance of the proposed model is much better than existing color image segmentation methods.