1. A gaze position estimation system, comprising: a photographing unit that photographs a face of a user who is looking at a screen displayed on a display unit; an area detecting unit that detects, from a photographed image of the photographing unit, an eye area of the user and at least one of a face area of the user or a predetermined part area of the user, the predetermined part area being an area of a predetermined part of the user other than the user's eyes; an areal size/position information obtaining unit that obtains areal size information and position information of the eye area, and areal size information and position information of the at least one of the face area or the predetermined part area; and a gaze position estimation unit that estimates a position in the screen that the user is gazing at, based on the areal size information and the position information that are obtained by the areal size/position information obtaining unit.