A $Y_1Ba_2Cu_3O_{7-delta}$ square spiral microstrip antenna (YBCO antenna) was epitaxially grown on a $LaAlO_3$ substrate by laser ablation. Also fabricated was a gold square spiral microstrip antenna (gold antenna) having the same structure as that of the YBCO antenna in order to compare the properties of both antennas. Both the YBCO antenna and the gold antenna were operated in Ku (12-18 GHz) band, and their properties such as the return loss, SWR, power gain, and radiation patterns were investigated at 77 K. The return loss below -10 dB was obtained in two frequency ranges, i.e., 14.05-14.90 GHz, and 16-18 GHz for the YBCO antenna at 77 K (YBCO superconducting antenna), and in the frequency range of 15.05-17.60 GHz for the gold antenna at 77 K. The SWR bandwidths are 0.85 GHz and 2 GHz for the YBCO superconducting antenna, and 2.55 GHz for the gold antenna at 77 K. The gain improvement of the superconducting YBCO antenna over the gold antenna at 77 K was about 10 dB in the frequency range of 16 GHz to 18 GHz. The radiation patterns show the YBCO superconducting antenna has the omni-directional property of a spiral antenna.