Cubic equations of state (EOSs) are widely used to model the thermodynamic properties of pure fluids and mixtures. However, because they fail to account for the long-range fluctuations existing in a fluid near the critical point, they do not accurately predict the fluid properties in the critical region. Recently, an approximate renormalization group method was developed that can account for these fluctuations. A similar method is applied to provide corrections to a generalized cubic EOS for pure fluids, which is able to represent all classic cubic EOSs. The proposed approach requires two additional parameters: <(c)over bar(RG)> and Delta. The value of <(c)over bar(RG)> is correlated to experimental critical compressibility data, while Delta is set equal to 1. The method is applied to predict the saturated liquid density of fluids of different polarity, and the corrections to the original EOS are found to significantly improve the predictions of this property both far from and close to the critical point. Finally, a correlation is presented for the direct evaluation of the parameter <(c)over bar(RG)> from the value of the critical compressibility factor.