This paper describes a new method for detecting the gaze position of a user on a monitor from monocular images. In order to detect the gaze position, we extract facial features (both eyes, nostrils and lip corners) automatically in 2D camera images and estimate the 3D depth information and the initial 3D positions of those features by recursive estimation algorithm in starting images. Then, when a user moves his/her head in order to gaze at one position on a monitor, the moved 3D positions of those features can be estimated from 3D motion estimation by Extended Kalman Filter (EKF) and affine transform. Finally, the gaze position on a monitor is calculated from the normal vector of the plane determined by those moved 3D positions of features. Especially, in order to obtain the exact 3D depth and positions of initial feature points, we unify three coordinate systems (face, monitor and camera coordinate system) based on perspective transformation. As experimental results, the 3D depth and the position estimation error of initial feature points, which is the RMS error between the estimated initial 3D feature positions and the real positions (measured by 3D position tracker sensor) is about 1.28 cm (0.75 cm in X axis, 0.85 cm in Y axis, 0.6 cm in Z axis) and the 3D motion estimation errors of feature points by Extended Kalman Filter (EKF) are about 3.6 degrees and 1.4 cm in rotation and translation, respectively. From that, we can obtain the gaze position on a monitor (17 inches) and the gaze position accuracy between the calculated positions and the real ones is about 2.1 inches of RMS error.