Gibbs ensemble Monte Carlo simulations were performed to calculate the vapor-liquid coexistence properties for the binary mixtures $CO_2/CH_3OH$, $CO_2/C_2H_5OH$, and $CO_2/CH_3CH_2CH_2OH.$ The configurational bias Monte Carlo method was used in the simulation of alcohol. Density of the mixture, composition of the mixture, the pressure-composition diagram, and the radial distribution function were calculated at vapor-liquid equilibrium. The composition and the density of both vapor and liquid from simulation agree considerably well with the experimental values over a wide range of pressures. The radial distribution functions in the liquid mixtures show that $CO_2$ molecules interact more stogly with methyl group than methylene group of $C_2H_5OH$ and $CH_3CH_2CH_2OH$ due to the steric effects of the alcohol molecules.