A physically well behaved analytical potential of a diatomic system is constructed based on perturbation theory and a potential correction to the Murrell-Sorbie potential. Alternative formulae for rotational constants and ro-vibrational energies are suggested. An energy-consistent method is proposed for calculating accurate potential energy curves of diatomic states. Applications of this method to the electronic states X 1Σ+g, C 1Πu, a 3Σ+g, e 3Σ+u of H2, the ground state X 1Σ+g of N2, and the states X 3Σ−g, C 1Σ−u, B 3Σ−u of the O2 molecule show that the present potential agrees excellently with the known Ryderberg-Klein-Rees data or accurate configurationinteraction (CI) studies, and is better than other analytical and some CI potentials, particularly for molecular electronic excited states.