The rates of evaporation and condensation of methanol under the vapor-liquid equilibrium condition at the temperature of 300 and 350 K are investigated with a molecular dynamics computer simulation. Compared with the argon system (reported in part I), the ratio of self-reflection is similar (similar to 10%), but the ratio of molecule exchange is several times larger than the argon, which suggests that the conventional assumption of condensation as a unimolecular process completely fails for associating fluids. The resulting total condensation coefficient is 20%-25%, and has a quantitative agreement with a recent experiment. The temperature dependence of the evaporation-condensation behavior is not significant.