At different thermodynamic temperatures (between 0.01 and 4000 K), the relaxation properties of three kinds of graphene nanoribbons with different aspect ratios are simulated by molecular dynamics method based on Tersoff-Brenner and AIREBO potential functions separately. Then we compare the energy curves and surface morphologies of nanoribbon relaxation with two kinds of potential functions, and study the dynamic equilibrium process of the graphene nanoribbons during their relaxation simulation. The simulation results show that the single layer graphene nanoribbon is not of a perfect planar structure and that a certain degree of fluctuations and folds occur at the edges and inside of nanoribbons, which are consistent with the existing experimental results; the surface fluctuation level of graphene nanoribbons decreases with the reduction of the aspect ratio, and the system kinetic energy has a dramatic influence on the relaxation deformation of the graphene nanoribbons at different temperatures, which indicates that the higher the system temperature, the greater the deformation is. Curl phenomenon could appear even on the surface of the nanoribbon with a high aspect ratio at a certain temperature. Finally, the simulations of graphen molecular dynamics by using the Tersoff-Brenner and AIREBO potential are deeply analyzed.