An improved simple generalized three-parameter cubic equation of state for pure fluids is proposed to estimate pure component fluid properties by incorporating substance dependent epsilon-function and almost substance independent sigma-function in the generic cubic equation of state, followed by temperature and acentric factor dependent attractive term. The proposed cubic equation of state is utilized to predict critical compressibility factor, liquid molar volume, vapor molar volume, and pure component vapor pressure for several simple hydrocarbons and fatty acid of methyl esters, and the predicted properties are compared with the actual values. In this study, most of the pure fluid properties are considered from literature; however experimentation is carried out for few fatty acid of methyl esters to determine pure fluid vapor pressure at elevated temperature and pressure. The proposed cubic equation of state is found to be accurate in predicting both literature reported and experimentally determined pure fluid properties. The overall performance of the proposed cubic equation of state is also compared with commonly used cubic equations of state and is found to be superior for predicting critical compressibility factors and other pure fluid properties.