The design method of a dual-polarized array antenna is investigated and presented in this communication. The antenna consists of a series-fed patch array (SFPA) antenna for vertically polarized (VP) radiation and a slotted microstrip first higher order mode (EH1-mode) periodic leaky-wave antenna (P-LWA) for horizontally polarized (HP) radiation. These two antennas are both analyzed by using the leaky-wave antenna method. It is revealed that the SFPA/EH1-mode element is expected to be operated under the short-/open-circuited condition, at which the desired VP/HP broadside radiation can be realized. Afterward, by reusing the radiator of the EH1-mode element as the ground of the SFPA one, the radiation apertures of these two elements can be designed in an overlapped style. Finally, a dual-polarized array antenna operated at 24.0 GHz is fabricated and tested for verification. The measurements demonstrate and validate that both the desired high-gain VP and HP radiation patters are achieved at broadside.