A graphene-based dual-band terahertz rectangular dielectric resonator antenna (DRA) is proposed in this work. The upper wall of the rectangular DRA is coated with graphene, which acts as an impedance surface to tune the resonant frequencies of the \({\varvec{T}\varvec{E}}_{111}^{\varvec{y}}\)and \({\varvec{T}\varvec{E}}_{113}^{\varvec{y}}\)modes of the antenna by varying its chemical potential. Also, it is observed that for some values of the chemical potential of graphene, the \({\varvec{T}\varvec{E}}_{113}^{\varvec{y}}\) mode is not well excited, which leads to the ability to reconfigure the antenna in terms of the number of operating bands. In another part of the paper, an approximate formula for obtaining the resonant frequency of the graphene-loaded DRA is presented for the first time. The resonance frequency results obtained from this theoretical method for different chemical potential values are compared with the simulation results, and it is concluded that there is a good agreement between them.