Graphene, a staggering material with amazing electrical properties is a unique solution for the implementation of Terahertz antenna. Graphene based patch antennas are gaining interest in the field of communication for its reduced size in micrometer range operating in the THz band. The selection of substrate material acts as a major performance controller as it regulates the resonant properties of the graphene patch antenna. A graphene based circular patch antenna is designed here for operating in the frequency range of 6.8–7.2 THz. We applied polyimide, quartz, silicon dioxide and silicon nitride as substrate materials and evaluated the performance of the patch antenna for individual substrate materials based on return loss, voltage standing wave ratio (VSWR), 3D and 2D radiation pattern with gain as output. The result shows that using polyimide as substrate material results in excellent performance with a gain of 16.7 dB as compared to other substrate materials.