Background: Eye tracking is a technology that detects the direction of the user's gaze in real time. This technology is used in various fields such as analyzing user emotions and behaviors by analyzing the length of time the gaze stays in a specific direction or the path of movement. Recently, Eye-gaze tracking is a popular to a non-contact interaction technique for the minimization of covid-19 infection. A study conducted in the past have a limitation in that the ocular rotational center point (ORCP) cannot be found in common. For this reason, each research is continuously researching to overcome this problem by using various sensors, structures, and phenomena. In spite of, a tiny movement of the subject cause an error in accuracy during the process of Eye-gaze tracking. In this paper, we propose a novel method for Eye-gaze tracking under the condition of photographing the front of the face using a camera. We named this position set as Human pupil orbit model (HPOM) and it can express as a spherical equation because it looks like a sphere in 3-dimensional coordinate.Results: A simulation experiment was performed to confirm the performance of the proposed method. The error of HPOM estimation appears under 1 pixel in the first experiment both ORCP and a radius. In addition, it was confirmed that the process of estimating HPOM can be conducted as a real time in the second experiment.Conclusions: The proposed method was able to overcome the common problem of existing studies that could not find the rotational center of an eye-ball. In addition, HPOM may be secured in real time even if the subject moves.