An antenna pointing control apparatus and method that reduce a pointing error of an antenna having a two-axis gimbal structure. An antenna installed on a ship hull is controlled to point toward a satellite by an antenna pointing control apparatus having a two-axis mechanism. Movement of the ship hull are recognized every prescribed cycle time, a satellite bearing is measured, and a pointing error of a directional antenna with respect to a satellite is detected. If it is determined that the satellite will not pass within a prescribed region A about an extension line of an azimuth angle (AZ) axis of the ship's hull, then a two-axis control is executed. However, if the satellite will pass within the prescribed region A, then a virtual three-axis control is executed.