It is difficult to obtain the accurate high-lying vibrational energies for most of the diatomic electronic states on modern experiments or theoretical computations based on quantum mechanics. Based on the new analytical formula for dissociation energy and algebraic method (AM) generated by Sun et al., the second order perturbation theory are used to study the full vibritional energies{EAMυ} and dissociation energies of the Li2－33Σ+g,Li2－13Δg,Li2－23Πg,Na2－B1Πu and K2－41Σ+g electronic states. The obtained results not only agree well with the experimental data for the low-lying vibrational energies, but also give all high-lying vibrational energies which are still difficult to obtain by experiment at present. These results supply necessary data for the studies which need high-lying vibrational energies and dissociation energies of diatomic alkali-metal molecule.