We propose a new thermodynamic approach for nonspherical molecules by applying a perturbation theory in which an anisotropic intermolecular potential, the hard Gaussian overlap, is the reference system. The new equation of state (EoS) modifies the usual statistical associating fluid theory (SAFT) approach by combining both segment and chain contributions as a single anisotropic term. Fluid particles are represented as ellipsoids rather than a set of a few tangential spherical segments. The perturbed potential is taken as a square well, following the original formulation of SAFT with attractive potential of variable range (SAFT-VR SW). The parameters of the proposed model were optimized to fit vapor pressures and saturated liquid densities for ethane and carbon dioxide. Derivative properties, such as isobaric and isochoric heat capacities, speed of sound, Joule-Thomson coefficient, thermal expansion coefficient, and isothermal compressibility, were evaluated at supercritical conditions up to 70 MPa for ethane and 200 MPa for carbon dioxide. The proposed EoS outperforms the original SAFT-VR SW EoS for many of these properties. This implies that an ellipsoidal geometry is an adequate representation of such nonspherical molecules, avoiding the approximations usually applied in Wertheim's first-order thermodynamic perturbation theory for the calculation of the Helmholtz free energy of chain formation.