Based on the thermodynamic perturbation theory of Wertheim, statistical associating fluid theory (SAFT) has became a successful equation of state for the description of thermodynamic properties of fluids, especially for systems including polymers. In recent years, different versions of SAFT have been developed based on square-well and Lennard-Jones reference fluids and improvements are achieved. In this paper SAFT is modified with two improvements in order to calculate the properties near the critical points of non-polar fluids. One improvement is the consideration of the segment shape in chain molecules using the hard convex body equation of state as the reference term and the relative expression for chain formation with the radial distribution function of hard convex body fluid is also included. The another improvement is the exclusion of the dispersion energy between intramolecular segments with a newly derived term based on the perturbation theory. The first improvement gives a better prediction of the critical points for one-segment non-spherical molecules and the second for chain molecules. The new equation of state includes four parameters for every non-polar fluid: the segment number m, the segment non-spherical parameter Ce. the segment volume nu (00) and the segment interaction parameter u(0). The saturated pressures and saturated liquid densities up to the critical point can be calculated with average absolute deviations of 0.6 and 0.8% for 44 non-polar fluids including n-alkanes, branched alkanes, cycloalkanes, alkenes, alkynes and aromatics. Critical temperatures, pressures and densities are calculated with the average absolute deviations of 0.2, 1.2 and 2.9%. The new equation of state was used to predict such thermodynamic properties as PVT lines, and vaporization enthalpies. The prediction results are also in good agreement with experimental data from literature.