Abstract: Ever since the concept of Quantum Computing (QC) was proposed, it has become a powerful tool to solve complex problems that classical computers are not able to tackle. There is still growing interest in the application of QC. Nevertheless, the quick and astonishing progress of Quantum Simulation (QS) has had a big impact on many domains, including how we perform quantum chemical simulations. The dynamic of a molecule can easily affect the properties of the system and therefore been a hot topic. Besides that, the vibrational states of molecules can represent qubits and are becoming a potential model for building a real quantum computer. The dynamics of the stretch vibrations of molecules have been studied extensively with mid- infrared spectroscopic techniques. The bending mode, another kind of vibration mode, has not been studied using quantum techniques. In this thesis, we discussed the model of a triatomic molecule and put emphasis on the Local Mode (LM) and Normal Mode (NM) transform, which are two perspectives of understanding the vibration of molecules. Then, we introduce a good accelerator for quantum simulation on molecule dynamics, which is Shortcuts to Adiabaticity (STA). By carrying out the calculations and applying them to quantum circuits, we successfully simulate a bond-angle-changing process of molecules with shorter time and shallower layer, and indeed realize the transform between LM and NM by quantum gates. In addition, we succeed in simulating the excited states of a triatomic system, paving the road for the calculation of larger molecules. After this work, we believe exploring bigger system-size molecules is feasible.