Eye tracker is a new apparatus of human-computer interaction, which has caught much attention in recent years. Eye tracking technology is to obtain the current subject’s "visual attention (gaze)” direction by using mechanical, electronic, optical, image processing and other means of detection. While the mapping function is one of the key technology of the image processing, and is also the determination of the accuracy of the whole eye tracker system. In this paper, we present a new mapping model based on the relationship among the eyes, the camera and the screen that the eye gazed. Firstly, according to the geometrical relationship among the eyes, the camera and the screen, the framework of mapping function between the pupil center and the screen coordinate is constructed. Secondly, in order to simplify the vectors inversion of the mapping function, the coordinate of the eyes, the camera and screen was modeled by the coaxial model systems. In order to verify the mapping function, corresponding experiment was implemented. It is also compared with the traditional quadratic polynomial function. And the results show that our approach can improve the accuracy of the determination of the gazing point. Comparing with other methods, this mapping function is simple and valid.