Abstract: As for diatomic molecular system, the characteristics of simple structure and abundant energy spectrum makes it become the touchstone of various theoretical models of quantum mechanics and the basic research tools of many derived applications. It plays an important role in precision measurement, quantum manipulation (such as ultra-cold molecules) and other frontier research fields. This review mainly focuses on the progress in precise vibration energy spectrum of diatomic molecules in recent years. The variational algebraic method (VAM) proposed by Weiguo Sun's group is described in detail. The advantages and limitations of this method are discussed by analyzing the full vibration energy spectrum of PO molecule. Finally, by incorporating the method into a more general data-driven research paradigm, the probable development direction of the VAM method is presented in this paper, which may provide new inspiration and ideas for obtaining higher precision vibration energy spectra of diatomic molecule.