A parameter-free analytical formula for dissociation energy of diatomic system is suggested recently by Sun et al. Together with the algebraic method (AM) which was presented to obtain accurate full vibrational energies for diatomic molecules in their previous work，the new formula is applied to study the dissociation energies and the full vibrational spectra of some diatomic ions in this work. The results show that the AM vibrational spectra and dissociation energies have excellent agreement with experimental values.