Existing methods for tracking three-dimensional (3-D) eye positions with a monocular color camera mostly rely on a generic 3-D face model and a certain face database. However, the performance of these methods is susceptible to the variations of head poses. For this reason, existing methods for estimating 3-D eye position from a single two-dimensional face image may yield erroneous results. To improve the accuracy of 3-D eye position trackers using a monocular camera, we present a compensation method as a postprocessing technique. We address the problem of determining an optimal registration function for fitting 3-D data consisting of the inaccurate estimates from the eye position tracker and their corresponding ground truths. To obtain the ground truths of 3-D eye positions, we propose two different systems by combining an optical motion capture system and checkerboards, which construct the form of the hand-eye and robot-world calibration. By solving a least-squares optimization problem, we can determine the optimal registration function in an affine form. Real experiments demonstrate that the proposed method can considerably improve the accuracy of 3-D eye position trackers using a single color camera.