A fourth order virial equation of state (VEOS) having a closed form was developed by solving cluster integrals with a semi-soft core (SSC) potential function. Three-body interaction was considered by the third and fourth order perturbation of the triple dipole interactions. Monte Carlo simulations for the two-body potential were carried out for three different temperature regions and comparison with the fourth order VEOS confirmed that the applicable reduced density range was enlarged to about 1.5 fold than the third order VEOS in the supercritical temperature region. The volumetric properties of argon and methane were calculated using the various versions of developed VEOS. The results were very accurate in the vapor region up to 100 bar and the predicted critical point was slightly better than that of the VEOS with a Lennard-Jones 12-6 potential function in literature. The accuracy of the developed VEOS was better than that of the empirical VEOS for nonpolar gases, which demonstrates the possibility of application in various fields. (c) 2012 Elsevier B.V. All rights reserved.