The prewetting transition of Ar adsorbed on a planar structureless Li surface was investigated using the density-functional theory, In the theoretical model, the renormalization-group transform and the three-body intermolecular interactions were considered. To describe the thermodynamic properties of Ar, a reliable ab initio potential was applied to model the interactions between Ar atoms and Li surface. The thin-film-thick-film coexistence diagram for prewetting transition was calculated. The prewetting critical temperature ͑upper boundary of prewetting transition͒ is found to be lower than those previous predictions. With the difference of thickness between the thin and the thick films served as the order parameter, the predicted prewetting critical exponent  is 0.175Ϯ 0.018. The value is close to the two-dimensional Ising value, demonstrating the predicted upper boundary is reliable. The wetting temperature ͑lower boundary of prewetting transition͒ was determined by two different methods: extrapolation of the chemical difference and evaluation of the contact angle via Young's equation, and nearly the same results are obtained. The convergence of the two methods further validates that the lower boundary is also correct. The wetting temperature is also found to be lower than those previous predictions.