This research presents a theoretical investigation on the performance of a vapour compression refrigerating system using different mixtures of Hydrocarbons and Hydrofluorocarbons refrigerants as a refrigerant. Genetic Algorithm method was used to solve a nonlinear constrained optimization problem for the selection of the best blend. The performance of new mixtures of Hydrocarbons and Hydrofluorocarbons refrigerants is compared with the performance of R-134a. The optimal solution of the new blend is has an improvement of 11.9% in the coefficient of performance over the currently used blend of R134a.