In this paper, we study the electronic conductance of the flat and bent armchair and zigzag graphene nanoribbons in the presence and absence of an external magnetic field within the nearest neighbor tight-binding approach. For the armchair case, we reduce the Hamiltonian of each benzene ring including the treated magnetic flux to the Hamiltonian of a two atomic molecule by using the renormalization method. Also, consider the effect of magnetic field by inserting the flux dependent phase coefficients in the corresponding hopping energies in the problem. Finally, we perform the numerical calculations related to the transmission coefficient by the means of the Green’s function technique within the Landauer approach. The results show that the applying an external magnetic field on the armchair nanoribbon creates some extra gaps in the conductance spectra. The widths of these gaps depend on the amount of nanoribbon bending. Furthermore, the value of conductance in the central gap for armchair case is more sensitive on the bending and magnetic field amounts with respect to zigzag case.