Motivated by recent studies on the use of graphene for new concepts of electronic/spintronic devices, the authors develop an efficient calculation method based on the nonequilibrium Green’s function to solve the quantum relativisticlike Dirac’s equation that governs the low-energy excited states in graphene. The approach is then applied to investigate the electronic transport and the spin polarization in a single-graphene barrier structure. The obtained results are presented and analyzed in detail aiming to highlight typical properties of the considered graphene structure as well as the efficiency of the developed approach that both may be helpful for further development in electronic devices and in spintronics.