In the dielectric response function method, the equation of state and thermodynamic properties of plasma can be calculated by defining the effective potential. In this method, it is necessary to determine the extent of its effect on plasma with the help of a suitable primary potential, and then the effective potential is determined by applying these effects. In this paper, for the first time, the Hulthen potential is used as the primary potential in describing hot dense plasma by the dielectric response function method. For this reason, to find a suitable relation between the screening parameters of Hulthen potential, De, and the Debye shielding parameter, μD, a comparison is made between the two potentials Hulthen and Debye. With this comparison, the parameter De is known and specified for each specific value of the coupling (Γ) and density (rs) parameters. The Hulthen potential with the specified screening parameter using the dielectric response function method is used to achieve the effective interaction potential for hot dense plasma. In the following, the equation of different states of fully ionized plasma is defined using the effective potential and the analytical calculation of the internal energy of the plasma particles is determined. Finally, the thermodynamic properties of hot dense plasma such as; free energy, pressure, specific heat, entropy, and enthalpy energy of the plasma system are calculated analytically.
