The aim of this paper is to study graphene plasmonics for THz applications. The range of absorbance of electromagnetic waves on a graphene monolayer is investigated to understand the plasmonic behaviour of graphene on patterned SiO2 substrate. Simulation results show that absorption range and intensity gets altered according to the graphene doping level, periodicity of grating and dielectric media used on the patterned substrate. These results show the plasmonic effect on graphene has a tuneable behaviour, and it can be utilised for the future plasmonic sensors and optoelectronics devices in the mid-infrared region. © 2017 IEEE.