In this communication, an $8 \times 8$ dual-polarized traveling-wave antenna array is proposed and studied for in-band full-duplex applications. The proposed array consists of single-layer dual-polarized patch antennas with a simple feeding network. Despite the strong coupling among antenna elements, good suppression for the self-interference can be achieved by using differential feedings. To validate the study, an on-board prototype is developed, fabricated, and measured. The results show that good impedance matching responses are found, and high isolation of over 50 dB between the dual-polarized outputs is realized from less than 13.0 to 15.7 GHz. Meanwhile, small sidelobes and low cross-polarization levels with low insertion loss are observed, showing well-designed radiation responses.