The present invention relates to an antenna apparatus for a moving object. It comprises a casing mountable on a moving object and a base plate rotatably supported for rotation about a first rotary shaft which is fixed to the casing. A first drive is provided for rotatably driving the base plate about the first rotary shaft. An antenna unit includes a first antenna plate having a predetermined first beam axis, a second antenna plate having a predetermined second beam axis and connecting member for connecting the first and second antenna plates, with the first and second beam axes being oriented parallel to each other and with the antenna plates being positioned at a predetermined fixed offset distance between them along a line which is parallel to the first and second beam axes. The antenna unit is rotatable about a second rotary shaft perpendicular to the first rotary shaft and second drive is provided for rotatably driving the antenna unit about the second rotary shaft perpendicular to said first rotary shaft.