We have proposed a novel geometric model of the eye in order to avoid the problems faced while using the conventional spherical model of the cornea for three dimensional (3D) model-based gaze estimation. The proposed model models the eye, including the boundary region of the cornea, as a general surface of revolution about the optical axis of the eye. Furthermore, a method for calculating the point of gaze (POG) on the basis of our model has been proposed. A prototype system for estimating the POG was developed using this method. The average root mean square errors (RMSEs) of the proposed method were experimentally found to be smaller than those of the gaze estimation method that is based on a spherical model of the cornea.