The core technology of visible-spectrum gaze tracker (VSGT) is the determination of the limbus circle on the eye image. The high complexity of analyzing eye images comes from various projection shapes of the eyeball and illumination conditions. In this thesis, we proposed an eyeball model construction method and refined iris matching equation to improve the system accuracy and the precision. In addition, a parallel computing architecture incorporating with a hierarchical search scheme for real-time limbus circle matching has been presented. The experimental result shows that the proposed model construction method significantly improves the overall eyeball model matching performance. The proposed hierarchical search scheme efficiently determines the optimal match model for an input eye image, and the proposed parallel computing architecture could be applied to the design of a high speed VSGT with the frame rate higher than 4000 frames/s.