An antenna apparatus that executes a pointing control so as to point a directional antenna installed on a mobile body toward a satellite, the antenna pointing control apparatus having a two-axis structure and comprising: a support member supporting the directional antenna rotatably about an elevation axis; a base pedestal supporting the directional antenna and the support member, the base pedestal being rotatable about an azimuth axis; an elevation axis rotating means for rotationally driving the directional antenna about the elevation axis; an azimuth axis rotating means for rotationally driving the directional antenna, the support member, and the base pedestal about the azimuth axis; a recording means (520, 530) for recognizing and recording movement and rocking of the mobile body once per prescribed cycle period; a measuring means for measuring a satellite bearing; an error detecting means for detecting a pointing error of the directional antenna based on a measurement result from the measuring means; and control means for controlling the elevation axis and the azimuth axis using a two-axis control, characterized in that: a determining means is provided which is arranged to determine whether or not the satellite will pass within a prescribed region about an extension line of the azimuth axis of the mobile body based on the measurement result from the measuring means and a record from the recording means; the determining means is arranged to issue an instruction to control the elevation axis and the azimuth axis using a two-axis control in accordance with the pointing error from the error detecting means if the determining means determines that the satellite will not pass within the prescribed region about the extension line of the azimuth axis of the mobile body; the determining means is arranged to issue an instruction to operate the azimuth axis rotating means and the elevation axis rotating means based on a virtual three-axis control if the determining means determines that the satellite will pass within the prescribed region about the extension line of the azimuth axis of the mobile body; and the control means is arranged to operate the azimuth axis rotating means and the elevation axis rotating means based on the virtual three-axis control if the determining means determines that the satellite will pass within the prescribed region, wherein the virtual three-axis control assumes that a virtual cross elevation axis (EL') exists, the virtual cross elevation axis extending in a direction perpendicular to the elevation axis, although a drive apparatus for the virtual cross elevation axis is not provided, and the virtual three-axis control controls the elevation axis and the azimuth axis in accordance with the pointing error from the error detecting means. a support member supporting the directional antenna rotatably about an elevation axis; a base pedestal supporting the directional antenna and the support member, the base pedestal being rotatable about an azimuth axis; an elevation axis rotating means for rotationally driving the directional antenna about the elevation axis; an azimuth axis rotating means for rotationally driving the directional antenna, the support member, and the base pedestal about the azimuth axis; a recording means (520, 530) for recognizing and recording movement and rocking of the mobile body once per prescribed cycle period; a measuring means for measuring a satellite bearing; an error detecting means for detecting a pointing error of the directional antenna based on a measurement result from the measuring means; and control means for controlling the elevation axis and the azimuth axis using a two-axis control, a determining means is provided which is arranged to determine whether or not the satellite will pass within a prescribed region about an extension line of the azimuth axis of the mobile body based on the measurement result from the measuring means and a record from the recording means; the determining means is arranged to issue an instruction to control the elevation axis and the azimuth axis using a two-axis control in accordance with the pointing error from the error detecting means if the determining means determines that the satellite will not pass within the prescribed region about the extension line of the azimuth axis of the mobile body; the determining means is arranged to issue an instruction to operate the azimuth axis rotating means and the elevation axis rotating means based on a virtual three-axis control if the determining means determines that the satellite will pass within the prescribed region about the extension line of the azimuth axis of the mobile body; and the control means is arranged to operate the azimuth axis rotating means and the elevation axis rotating means based on the virtual three-axis control if the determining means determines that the satellite will pass within the prescribed region,