Gaze-on-screen tracking, an appearance-based eye-tracking task, has drawn significant interest in recent years. While learning-based high-precision eye-tracking methods have been designed in the past, the complex pre-training and high computation in neural network-based deep models restrict their applicability in mobile devices. Moreover, as the display frame rate of mobile devices has steadily increased to 120 fps, high-frame-rate eye tracking becomes increasingly challenging. In this work, we tackle the tracking efficiency challenge and introduce GazeHFR, a biologic-inspired eyetracking model specialized for mobile devices, offering both high accuracy and efficiency. Specifically, GazeHFR classifies the eye movement into two distinct phases, i.e., saccade and smooth pursuit, and leverages inter-frame motion information combined with lightweight learning models tailored to each movement phase to deliver high-efficient eye tracking without affecting accuracy. Compared to prior art, Gaze-HFR achieves approximately 7x speedup and 15% accuracy improvement on mobile devices. Index Termsgaze estimation, mobile imaging, biomedical video analysis, applications of machine learning * indicates an equal contribution. † indicates the corresponding author