In the present work, the thermodynamic of dense fluids, both compressed liquids and dense supercritical fluids, has been modeled, solely, based on the contribution of attraction of effective pair potential. The intermolecular interaction is modeled by the hard-core Yukawa potential (HCY) as an effective pair potential (EPP) with temperature dependent hard-core diameter. Using this EPP in the exact thermodynamic relations, an equation of state (EoS) for the compressibility factor of dense fluid has been derived. This EoS shows that (Z - Z(cs)) as function of p(1/3) must be linear for each isotherm of fluid where Zcs is the compressibility factor of the reference fluid (Carnahan-Starling (CS) EoS) with temperature-dependent hard-core diameter and Z is the experimental compressibility factor of fluid. To our knowledge, this is the first report on this new regularity for dense fluids only based on the perturbation theory in literature. The validity of this regularity has been tested for different fluids including Ar, Kr, Ne, H-2, N-2, NH3, NF3, CH4, C2H2, C3H8, C2H6, C2H4 and CH3OH. This regularity is valid for densities greater than pB, where pB is the Boyle density. Finally, using the proposed regularity, the values of the EPP parameters for the mentioned fluids were obtained at different temperatures. (c) 2015 Elsevier B.V. All rights reserved.