To date, it has been considered that all classical equations of state (EOS) have failed to describe the properties of fluids near the critical region, where the density fluctuations have a significant influence on fluid properties. In this paper, we suggest a newly constructed equation for fluid states, the generalized van der Waals (GvdW) EOS with the highly simplified Dieterici's form P = [RT/(V - b)] - a(b/V)c by a new model potential construction describing intermolecular interactions. On the basis of the model potential construction, it is shown that the a, b, and c parameters have physical interpretations as an internal pressure, a void volume, and a dimensionless value that represents an inharmonic intermolecular cell potential, respectively. As an illustration of our model approach, we initially apply it to near the critical point (cp) region, where all classical EOS descriptions have been incorporated with experimental thermodynamic data, and we obtain a table of three parameters for 12 pure normal fluids, which precisely describes thermodynamic critical values. On the basis of the basic relations between pressure and volume at the critical point, we express the corresponding EOS in terms of the c parameter, and by this means, we also obtain a theoretical vapor-liquid equilibrium (VLE) line, which closely coincides with the experimental data for several pure normal fluids near the critical region. As a result, we show that thermodynamic properties near the critical region can be described analytically by only three parameters. In addition, to validate our EOS for the temperature-differential derivatives, we show that the calculated isochoric heat capacity (Cv) of saturated argon closely coincides with the experimental data. Moreover, the possibility of a precise description with respect to the entire fluid region is also argued, in terms of the physical cases from the triple point to the ideal gas region.