Abstract: A parameter-free analytical formula for dissociation energy of diatomic system is proposed recently by Sun et al..The new formula, which can be used together with algebraic method (AM) to calculate the accurate full vibration energy for diatomic molecules, is applied to study the dissociation energy and the full vibration spectra of the X²Σ_g⁺ state of Li₂⁺ and the X²Σ⁺ state of CO⁺ diatomic ions.The results show that the AM vibration spectra and dissociation energy have excellent agreement with experimental values.