Thispaperobtainsaccuratevibrationalspectroscopicconstantsandfullvibrationalenergyspectrumbythealgebraicmethod(AM)forsomeelectronicstatesofhalogendiatomicmolecules.MotivatedbytherecentsuccessofobtainingthedissociationenergiesofLi2moleculebyusinganewanalyticalformula,itfurtherextendstheformulatostudythedissociationenergiesofhalogendiatomicmolecules.TheresultsshowthattheAMspectrumandthetheoreticaldissociationenergiesagreewellwithRKRdataandexperimentaldatarespectively.