NVT- and NpT-Gibbs ensemble Monte Carlo (GEMC) simulations were applied to describe the vapor-liquid equilibrium of water (between 323 and 573 K), carbon dioxide (between 230 and 290 K) and their binary mixtures (between 348 and 393 K). The properties of supercritical carbon dioxide were determined between 310 and 520 K by NpT-MC simulations. Literature data for the effective pair potentials (for water: the SPC-, SPC/E-, and TIP4P potential models; for carbon dioxide: the EPM2 potential model) were used to describe the properties of the pure substances. The vapor pressures of water and carbon dioxide are calculated. For water, the SPC- and TIP4P models give superior results for the vapor pressure when compared to the SPC/E model. The vapor-liquid equilibrium of the binary mixture, carbon dioxide-water, was predicted using the SPC- as well as the TIP4P model for water and the EPM2 model for carbon dioxide. The interactions between carbon dioxide and water were estimated from the pair potentials of the pure components using common mixing rules without any adjustable binary parameter. Agreement of the predicted data for the compositions of the coexisting phases in vapor-liquid equilibrium and experimental results is observed within the statistical uncertainties of the simulation results in the investigated range of state, i.e. at pressures up to about 20 MPa,