We have studied the charge and thermal transport properties of a porphyrin-based single-molecule transistor with electro-burnt graphene electrodes (EBG) using the nonequilibrium Green’s function method and density functional theory. The porphyrin-based molecule is bound to the EBG electrodes by planar aromatic anchor groups. Due to the efficient π–π overlap between the anchor groups and graphene and the location of frontier orbitals relative to the EBG Fermi energy, we predict HOMO-dominated transport. An on–off ratio as high as 150 is predicted for the device, which could be utilized with small gate voltages in the range of ±0.1 V. A positive thermopower of +280 μV/K is predicted for the device at the theoretical Fermi energy. The sign of the thermopower could be changed by tuning the Fermi energy. By gating the junction and changing the Fermi energy by +10 meV, this can be further enhanced to +475 μV/K. Although the electrodes and molecule are symmetric, the junction itself can be asymmetric due to different binding configurations at the electrodes. This can lead to rectification in the current–voltage characteristic of the junction.