Recently, the demand for the mobile satellite communication has been increasing, and various communication services are in the planning stage. Different types of vehicle antennas, which are able to track satellites, have been studied. A candidate for this request is the beam tracking patch array antenna with a square shape. The advantages are its reduced bulk and low price. In this paper, we especially study two circularly polarized beam-switching array antennas respectively composed of 3 and 4 elements having a single-point feed in terms of numerical simulations. The numerical simulations have been performed in the 2.6 GHz frequency band reserved to the mobile satellite broadcasting. Good performances in terms of gain and axial ratio have been obtained.