Equilibrium parameters of ozone, such as equilibrium geometry structure parameters, force constants and dissociation energy are presented by CBS-Q ab initio calculations. The calculated equilibrium geometry structure parameters and energy are in agreement with the corresponding experimental values. The potential energy function of ozone with a C2v symmetry in the ground state is described by the simplified Sorbie-Murrell many-body expansion potential function according to the ozone molecule symmetry. The contour of bond stretching vibration potential of an O3 in the ground state, with a bond angle (θ) fixed, and the contour of O3 potential for O rotating around O1-O (R1), with O1-O bond length taken as the one at equilibrium, are plotted. Moreover, the potentials are analysed.