The Moller-Plesset perturbation approach, up to the complete fourth order, is employed to calculate the energy potential curve of the neon dimer interaction (R = 2.0-6.0 angstrom). A basis set of the energy-optimized 6-311G set extended with the sp-, d-, and f-type diffuse and polarization functions is used, and the the full function counterpoise correction for the basis set superposition error is applied. Hartree-Fock interaction energies and correlation interaction energies from the fourth-ordes Moller-Plesset perturbative calculations in the region of the van der Waals minimum are studied and compared to the available ab initio and other nonempirical results in the literature. The role of triple excitations for the correlation interaction energy is stressed and confirmed by the calculations. Converged and nearly converged interaction energies are achieved at the distances (R = 3.2-6.0 angstrom) beyond the van der Waals minimum, where about 90-100% of the total interaction energies are recovered by the complete fourth-order calculations. At shorter distances (R = 2.0-3.1 angstrom), the interaction energies are still considerably underestimated even at the complete fourth-order level, due mainly to the lack of higher than f polarization functions in the present basis set, instead of the truncation of the Moller-Plesset series. This work demonstrates that the complete fourth-order Moller-Plesset perturbation may be used as a reliable method for reasonably accurate calculations of van der Waals potentials.