The equilibrium geometries, potential energy curves, spectroscopic dissociation energies of the ground and low-lying electronic states of He-2, He-2(+) and He-2(++) are calculated using symmetry adapted cluster-configuration interaction (SAC/SAC-CI) method with the basis sets CC-PV5Z. The corresponding dissociation limits for all states are derived based on atomic and molecular reaction statics. The analytical potential energy functions of these states are fitted with Murrell-Sorbie potential energy function from our calculation results. The spectroscopic constants B-e, alpha(e), omega(e), and omega(e)chi(e) of these states are calculated through the relationship between spectroscopic data and analytical energy function, which are in well agreement with the experimental data. In addition, the origin of the energy barrier in the ground state X-1 Sigma(+)(g) of He-2(++) energy curve are explained using the avoided crossing rules of valence bond model.