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We propose a novel method for tracking eye gaze that allows natural head movement. Most existing remote eye gaze trackers cannot work under natural head movement due to the difficulty of building a gaze mapping function that can incorporate head motion information. Therefore, the user is required to hold his/her head unnaturally still, possibly with the use of chin-rest. In addition, before each usage of the tracking system, a cumbersome calibration procedure must be performed to obtain a gaze mapping function. Our proposed method significantly improves the conventional Pupil Center Corneal Refection (PCCR) technique to permit natural head movement and to minimize calibration. Support vector regression (SVR) is used to construct a highly nonlinear generalized gaze mapping function that accounts for head movement. As the head moves naturally in front of the camera, the associated gaze mapping function with each new head position will be obtained automatically by the learned generalized gaze mapping function. Once learned, the generalized gaze mapping function can be used by other users via a simple personal adaptation without retraining. Experiments for multiple users show that eye gaze can be estimated accurately under natural head movement via the proposed technique.