Modern experimental methods or accurate quantum theory methods usually may obtain a vibrational energy subset［Ev］ containing m energies, but it may be very difficult to have all the excited highlying vibrational energies f or the electronic states of most diatomic molecules. Since the full vibrational spectrum and the molecular dissociation energies of the electronic states of Na 2 molecule are very important in many studies and applications, the vibrationa l spectroscopic constants and the full vibrational spectra of some electronic st ates of Na2 molecules are acqnired using the algebraic method (AM), and the di ssociation energy (DE) of these states are obtained using the algebraic energy m ethod (AEM). The results show that AM can give accurate vibrational spectroscopi c constants and correct full vibrational energy spectrum {Ev} from experim ental vibrational energy subset［Ev］, and the molecular dissociation energies obtained using the AEM have much better accuracy than those generated u sing the vibrational constants given in the literature. The AEM can give reliabl e values of the dissociation energies for some excited electronic states whose D E may not be available in the literture.