A high-gain and tri-band terahertz microstrip antenna with a photonic band gap (PBG) substrate is presented in this paper for terahertz communications. Polyimide dielectric columns are inserted into the silicon substrate to form the PBG substrate to improve the gain of the antenna. The PBG substrate and polyimide substrate constituted a multilayer substrate structure and enabled the multi-band operation of the antenna. The PBG substrate antenna achieves gains of 6.28 dB, 4.84 dB, and 7.66 dB at resonant frequencies of 0.360 THz, 0.580 THz, and 0.692 THz, respectively, outperforming the homogeneous substrate THz microstrip antenna (H antenna) by 1.18 dB, 1.74 dB, and 1.82 dB, respectively. The radiation efficiencies at three operating bands are over 93%, 92%, and 88%, respectively, which are slightly higher than that of the H antenna and greater than that of the standard multi-band antenna.