This paper describes a sophisticated method to estimate visual direction using iris contours. This method requires only one monocular image taken by a camera with unknown focal length. In order to estimate the visual direction, we assume the visual directions of both eyes are parallel and iris boundaries are circles in 3D space. In this case, the two planes where the iris boundaries reside are also parallel. We estimate the normal vector of the two planes from the iris contours extracted from an input image by using an extended "two-circle" algorithm. Unlike most existing gaze estimation algorithms that require information about eye corners and heuristic knowledge about 3D structure of the eye in addition to the iris contours, our method uses two iris contours only. Another contribution of our method is the ability of estimating the focal length of the camera. It allows one to use a zoom lens to take images and the focal length can be adjusted at any time. The extensive experiments over simulated images and real images demonstrate the robustness and the effectiveness of our method.