We provide the design of a co-polarized simultaneous transmit and receive (STAR) array antenna, aiming to address the issue of undesired isolation in the antenna domain of the millimeter-wave (mm-Wave) full-duplex co-polarized communication system. As the cornerstone for the design and development of the antenna, the guided-wave structures of the virtual-electric-wall (VEW)-based ridge substrate-integrated waveguide (RSIW) and ridge parallel plate waveguide (RPPW) are proposed and applied to the full-duplex antenna design. Compared with conventional RSIW, VEW-based RSIW has the merits of lower ohmic loss and releasing the fabrication tolerance in the array antenna. Additionally, on the basis of parallel plate waveguide (PPW), the proposed RPPW exhibits a Chebyshev filtering response. The radiating part of the proposed array employs a slot-pair array excited along orthogonal directions by using the preceding guided-wave structures. Among them, the RSIW array serves as the Tx antenna, and the RPPW array is regarded as the Rx antenna. To achieve co-polarized radiation patterns in the boresight direction, the substrate-integrated waveguide (SIW) feed network is integrated into the reverse side of the antenna, providing differential and common-mode excitations for the RSIW-excited and RPPW-fed arrays. Furthermore, the inter-port isolation is effectively ameliorated by inserting the mushroom-type metamaterial between linear arrays. As a proof-of-concept, a shared-aperture full-duplex array operating in the Q-band is developed and fabricated to demonstrate the above concept by using standard printed circuited board technology. The measured overlapped impedance bandwidth covers from 38.18 GHz to 39.13 GHz. The measured Tx-to-Rx isolation is greater than 25.5dB in the Q-band. The measured peak gains in Tx- and Rx-mode are 18.4 dBi and 17.8 dBi. The simulation and measurement results show good consistency, verifying the effectiveness of the proposed array in inter-port isolation, array size, planarization, and lightweight, making it suitable for mm-Wave shared-aperture full-duplex communication systems.