This paper describes a conic-based algorithm for estimating visual line from a single monocular image. By assuming that the visual lines of the both eyes are parallel and the iris boundaries are circles, we propose a "two-circle" algorithm that can estimate the normal vector of the supporting plane of the iris boundaries, from which the visual line is calculated. Our new method does not use either the eye corners, or some heuristic knowledge about the structure of the eye. Another advantage of our algorithm is that a camera with an unknown focal length can be used without assuming the orthographical projection. This is a very useful feature because it allows one to use a zoom lens and to change the zooming factor whenever he or she likes. It also gives one more freedom of the camera setting because keeping the camera far from the eyes is not necessary in our method. The extensive experiments over simulated images and real images demonstrate the robustness and the effectiveness of our method.