Based on a new derived radial distribution function (RDF) for potentials with a hard-core we have presented in this paper a method to apply the derived RDF for calculating thermodynamic properties of real fluids up to moderate densities. In order to use the derived RDF for real fluids, one of the potential parameters is chosen in such a way that the RDF behaves more like that for a real fluid. Hence we have been able to calculate all thermodynamic properties of a simple fluid analytically. We have then applied our procedure to a Lennard-Jones fluid and compared the results with simulation data. The agreement is good up to moderate densities, i.e. rho* <= 0.6, which lies in the liquid range of Lennard-Jones fluid. We have also applied our method to a real fluid, i.e., argon. We supposed that argon is an example of a Lennard-Jones fluid. The calculated results are in good agreement with experimental data for gaseous state of argon. For the liquid state the agreement is not as good as that found for the gaseous fluid. (c) 2007 Elsevier B.V. All rights reserved.