Equations of state are vital tools for the calculation of gases and liquids properties. One of the most important EoSs is Virial EoS. One unique property of Viral EoS is that its coefficients, which are calculated from potential functions, are related to intermolecular forces. In this paper, Kihara potential function is improved based on molecular structure, and all coefficients are determined by optimization based on second Virial coefficient calculated from PVT data. A new parameter is introduced in this model which is representing the effective molecular diameter of molecules which is comparable with the calculated dimensions of molecules. The second Virial coefficient of 53 polar and non-polar molecules are calculated with the proposed potential function and classified into 5 groups based on the molecular structure. 1067 experimental data points of hydrocarbons including n-alkanes, alkenes, alcohols, chlorofluorocarbons (CFCs), hydrofluorocarbons (HFCs), Hydrochlorofluorocarbons (HCFCs), Trichloromethane, Dichloromethane, Chloromethane, 1,1,1-Trichloroethane, 1-Chlorobutane, branched alkanes, benzene, toluene, water and carbon dioxide were exploited. 610 experimental data points of the aforementioned substances were used to obtain the new model's coefficients, and the remaining data points were implemented to validate the proposed model. Additionally, the accuracy of the proposed model is compared with the other models such as Kihara, Exp-6, square-well, L-J and Stockmayer that the results reveal an enhanced accuracy. The total average absolute deviations for non-polar substances based on the proposed model, Kihara, Exp-6, square-well and L-J are 2.57, 3.14, 3.57, 2.90 and 7.85%, respectively. For polar substances, the total average absolute relative deviations based on the proposed model and Stockmayer are 3.95 and 6.69%, respectively. Also, Z compressibility factor, molar heat capacity and density of some polar and non-polar substances including water, methane, ethane, carbon dioxide, 1-butanol and 1,1,1,2-tetrafluoroethane are calculated to validate the proposed model, and the results showed that this model has good accuracy for calculation of the aforementioned properties in different temperature and pressure ranges. (C) 2019 Elsevier B.V. All rights reserved.