In experimental studies, hydrazine hydrate is widely employed as a reducing agent for the conversion of graphene oxide to graphene. Herein, we conducted theoretical calculations using cluster models to investigate the adsorption behavior of hydrazine hydrate on the surface of graphene. The calculated adsorption energy reveals that hydrazine hydrate can physically bind to the graphene surface. Our findings indicate that two hydrogen bonds stabilize the hydrazine hydrate molecule, while its adsorption onto the graphene surface is primarily driven by van der Waals forces. By combining computational simulations and experimental measurements, we thoroughly examined the Raman spectra of both free and adsorbed hydrazine hydrates, which enabled us to gain detailed insights into their molecular vibrations. Notably, in the Raman spectra of free hydrazine hydrate, a strong peak at around 3300 cm-1 corresponds to the NH2 vibration. Similarly, peaks near 3300 cm-1 were observed in the Raman spectra of graphene with adsorbed hydrazine hydrate molecules. The results are expected to provide valuable references for future experimental investigations involving hydrazine hydrate.