Iris center detection accuracy has great impact on eye gaze tracking system performance. This paper proposes an easy and efficient iris center detection method based on modeling the geometric relationship between the detected rough iris center and the two corners of the eye. The method fully considers four states of iris within the eye region, i.e. center, left, right, and upper. The proposed active edge detection algorithm is utilized to extract iris edge points for ellipse fitting. In addition, this paper also presents a predicted edge point algorithm to solve the decrease in ellipse fitting accuracy, when part of the iris becomes hidden from rolling into a nasal or temporal eye corner. The evaluated result of the method on our eye database shows the global average accuracy of 94.3%. Compared with existing methods, our method achieves the highest iris center detection accuracy. Additionally, in order to test the performance of the proposed method in gaze tracking, this paper presents the results of gaze estimation achieved by our eye gaze tracking system.