In this paper, the new excess Gibbs energy mixing rule, which coupled with the consistent form with the quadratic composition dependence of the second virial coefficient and the excess Gibbs energy (G(0)(E)) at standard zero pressure, has been developed. This proposed mixing rule, combining a Peng-Robinson equation of state with the analytical solutions of groups (ASOG) group contribution method, provide a Peng-Robinson group contribution method (PRASOG). The PRASOG model has predicted the high-pressure vapor-liquid equilibria (VLE) for binary systems containing alcohols, acetone, and water using the available ASOG group pair parameters determined at low pressure with good accuracy. The ASOG parameters have also been shown for 31 group pairs relating to two gas groups, CO2 and CH4, which indicate potential for global warming, using binary experimental high-pressure VLE data in the temperature range 200-600 K. High-pressure VLE have then been correlated for 56 binary systems containing carbon dioxide and/or methane. These results are compared with those of the predicted Soave-Redlich-Kwong (PSRK) and linear combination of the Vidal and Michelsen (LCVM) models. Finally, using the group pair parameters that have been determined from VLE data, solid-gas equilibria have been predicted with fairly good accuracy for eight binary and one ternary systems containing carbon dioxide.