Abstarct: Two-dimensional materials such as graphene are among the most important materials in which it is possible to have properties such as very high molecular strength, very good conductivity against heat and electricity and very high light absorption. Expansion of the structure in the nanowire channel in the direction perpendicular to the transport causes effects such as Dispersion. The most effective dispersion is caused by the non-uniform expansion of the two-dimensional structure, the presence of defects and impurities in the molecules that make it up. Molecular semiconductor devices are usually modeled with Green functions. As its computational structure expands due to the increase in atoms, for solving green matrices becomes very complex and use highly advanced supercomputers. In this research, the molecular structure of a graphene nanoribbon whose channel with armchair structure and its electrodes with zigzag edge structure is modeled and simulated by the unbalanced Green function model and the inclusion of dispersion effect in it with coherent transport system. The width of the canal is asymmetrically expanded in the range of 1.7 nm to 16.1 nm. The simulations were performed with two models, considering the dispersion effect and without the dispersion effect. Comparison of theoretical results with experimental measurements shows that the inclusion of the scattering model in the Green function reduces the simulation error in a wide-width structure from %89 to %9. This error is especially evident in the model with its dispersion when the channel width is more than 7 nm.