Patch material plays a significant role in controlling the performance and resonating frequency of patch based antennas. In this work, we compared graphene and copper nano-based patch antennas in terms of return loss, bandwidth, gain, directivity and voltage standing wave ratio (VSWR). The simulation is carried out using high frequency structure simulator HFSS. The substrate material used is Silicon dioxide. The antenna is designed to operate in the THz frequency band of (1-15THz) with the fundamental frequency of 5.5THz. The result shows that, the classical metallic antennas with copper material resonant at lower frequency of 3THz while graphene resonant at the higher frequency of 7THz, this is due to high electrons mobility in graphene than in copper. Graphene based patch antenna achieves maximum return loss of -24.4555dB with the corresponding VSWR of 1.0413. The maximum gain of 7.1943dB is achieved with a bandwidth of 522.3GHz; this shows better antenna performance than copper except the bandwidth. The contemporary copper antenna attains return loss of -14.7028dB with the corresponding VSWR of 3.2336. The gain of 4.6219dB is achieved with a bandwidth of 1188.5GHz. With this result, it can be seen that graphene is a suitable choice and can replace copper patch material for patch antennas for wireless applications in terahertz frequency band.