A 2.4 GHz dual-polarized antenna for a Doppler radar is studied. The proposed dual-polarized antenna using a stacked annular ring patch with two co-centric gap-coupled feed lines and a $90^{circ}$ hybrid exhibits fairly good performance of 22 dB isolation at a center frequency of 2.4 GHz. Using a $90^{circ}$ hybrid, a right-handed circular polarization for the transmitter and a left-handed circular polarization for the receiver are implemented. The gain of the designed antenna is about 0 dBi over operating frequencies. The antenna size including a ground plane is only $40{ imes}40;mm^2$.