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In this paper, a microstrip patch array antenna with high gain and wideband for dual transmitting/receiving at Ku-band is presented. The patch array antenna has a horizontal polarization for Rx band and a vertical polarization for Tx band. A unit element of the patch array antenna consists of one radiating patch and two parasitic patches for improving impedance bandwidth and gain characteristics, and Tx/Rx feed circuits for bidirectional communication. For obtaining high gain, the unit patch elements are arranged the form of a 1×8 array structure. To verify the practicality of this antenna, we fabricated a 1×8 microstrip patch array antenna and measured the antenna pattern. As a result, we obtain that the gain of the dual Tx/Rx array antenna is 17.1∼18.1 dBi at 11.7-12.75 GHz and 14.0-14.5 GHz. The impedance bandwidth is about 10% at Rx band and 11% at Tx band. The cross-polarization level is below -25dB, and the sidelobe level is below -9.4dB.