In view of the importance of the full vibrational spectrum and the molecular dissociation energies of K2 molecule to many studies and applications, this paper uses the SUN and REN's algebraic method (AM) which is based on perturbation theory and the algebraic energy method (AEM) based on the AM to study the vibrational spectroscopic constants, and the full vibrational spectra (Eυ) including the excited high-lying vibrational energies of electronic states X1Σ+g,a3Σ+u,0-g,B1Πu and 33Πg of K2 molecule, and obtain the accurate theoretical values of dissociation energies(De) of these states. The full vibrational spectra, especially the high-lying vibrational energies and dissociation energies, are difficult to determine experimentally, so this study can provides physical data for scientific research.