Recently, the research on graphene based microstrip patch antennas have made great progress. Hence a comparative study of copper and graphene based rectangular microstrip fed patch antennas is presented in this paper. Both single and 2×2 array microstrip patch antennas are designed. The considered performance parameters of the designed antenna are return loss, VSWR, bandwidth, gain, and directivity at a targeted resonance frequency of 2.45 GHz. Based on the results and analysis, it is noted that the graphene based single rectangular patch antenna shows higher performance than the copper based single rectangular patch antenna. And also graphene based 2×2 patch antenna array gives improved return loss, VSWR, bandwidth and gain than the copper based 2×2 patch antenna array.