The problem of 3D gaze estimation can be viewed as inferring the visual axes from eye images. It remains a challenge especially for the head-mounted gaze tracker (HMGT) with a simple camera setup due to the complexity of the human visual system. Although the mainstream regression-based methods could establish the mapping relationship between eye image features and the gaze point to calculate the visual axes, it may lead to inadequate fitting performance and appreciable extrapolation errors. Moreover, regression-based methods suffer from a degraded user experience because of the increased burden in recalibration procedures when slippage occurs between HMGT and head. To address these issues, a high-accuracy 3D gaze estimation method along with an efficient recalibration approach is proposed with head pose tracking in this paper. The two key parameters, eyeball center and camera optical center, are estimated in head frame with geometry-based method, so that a mapping relationship between two direction features is proposed to calculate the direction of the visual axis. As the direction features are formulated with the accurately estimated parameters, the complexity of mapping relationship could be reduced and a better fitting performance can be achieved. To prevent the noticeable extrapolation errors, direction features with uniform angular intervals for fitting the mapping are retrieved over human’s field of view. Additionally, an efficient single-point recalibration method is proposed with an updated eyeball coordinate system, which reduces the burden of calibration procedures significantly. Our experiment results show that the calibration and recalibration methods could improve the gaze estimation accuracy by 35 percent (from a mean error of 2.00 degrees to 1.31 degrees) and 30 percent (from a mean error of 2.00 degrees to 1.41 degrees), respectively, compared with the state-of-the-art methods.