Star acquisition is one of the most time-consuming routines in star-tracker operation. In the star image, a star point spread function (PSF) represents a near-Gaussian distribution. The star extraction consists in finding the highest-intensity pixel among the PSFs, collecting the adjacent pixels, and then calculating the star centroids in the star image plane. The candidate highest-intensity pixels are the maximum extremum points of the underlying intensity function of a digital star image. To extract star from the star image, the cubic facet model is applied to fit the underlying intensity surface in star acquisition procedure. A new extraction approach, using surface-fitting methods to approximate locally the image intensity function, and then using the partial derivatives of the fitted surface to make decisions regarding the maximum extremum points, is proposed. A number of experiments are carried out on simulated star images. The experimental results demonstrate that the proposed method is efficient and robust.