Abstarct: Distribution functions have an important role in the extensive and development of dense fluids theories. By using of these functions many of thermodynamic properties of dense fluid can be calculated. In recent years indicated that by using the core condition at computing the radial distribution function can be led to reduction of thermodynamic inconsistency. In this work have been tried to present analytical exxpression for radial distribution function by using the square-well potential and a kind of model for integral equation, in which the core condition has been observed and numerical solution of Ornstein-Zernike is available. Studies have been done on argon fluid and have been done survey on quality of radial distribution function at different thermodynamic state. Treatments of radial distribution function at different thermodynamic state have been considered and it's found that at super critical and near the critical point it's acceptable. For data point of radial distribution function at sub and super critical of argon fluid, analytical exxpression is obtained. And for square well potential width of the attractive well, is determined according to best result for internal energy at near the critical point so that 0.7 is found. By using these analytical exxpressions for radial distribution function have calculated the thermodynamic properties at different region and these properties compared with experimental data. According to this study it's found that this model is successful for prediction of internal energy and Helmholtz free energy near the critical temperature and the results for these properties has more accurate above the critical temperature. Also this model is successful for prediction of isothermal compressibility factor and compressibility factor.