Disclosed is a flexible display control apparatus. The flexible display control apparatus includes a measurement part which measures the viewing distance from both sides of a flexible display to the center part; a calculation part which uses the first viewing distance from the center part to a user in the measured viewing distance and calculates a target curvature for changing the present curvature of the flexible display; and a control part which changes the present curvature of the flexible display into the target curvature calculated by the calculation part. The present curvature of the flexible display can be changed according to the viewing distance between the flexible display and the user. Optimal view can be continuously provided even though the viewing distance of the user is changed.