There has been considerable interest in engaging porphyrin, which plays a central role in a variety of biological processes, as a molecular device for bio-inspired system application. This paper is focused on molecular junctions made up of porphine, the metal-free counterpart of porphyrin, and graphene electrode. Electronic properties are elucidated using the density functional theory and non-equilibrium Green’s function method. Excellent coupling between the porphine molecule and graphene electrode is obtained by carbon-carbon covalent bonding and has been analyzed by the electron difference density. The current-voltage curve and the evolution of the transmission spectrum with applied voltage bias have also been investigated. A noteworthy observation is the pronounced negative differential resistance (NDR) behavior, obtained when a benzene ring precisely bridges two porphine molecules. The projected device density of states and the potential profile along with the charge distribution at various applied voltages have been analyzed to understand the NDR behavior. The study confirms that the excess current in the NDR region can be attributed to resonant tunneling through the potential barrier.