We have presented a first-principles Simulation study of the vibrational spectral diffusion and hydrogen bond dynamics in an aqueous solution of N-Methylacetamide (NMA). We have studied the spectral diffusion of local OD stretch modes of deuterated water in the first hydration shells a the carbonyl (CO) and deuterated amide (ND) modes and their relations to the dynamics of hydrogen bonds formed by water with these groups. The frequency fluctuations of the amide I and amide A modes of the solute are also investigated. It is found that the vibrational spectral diffusion of water molecules in the first hydration shell of the carbonyl oxygen of NMA proceeds with three time scales: A short time relaxation (similar to 100 ft) originating from the dynamics of NMA-water hydrogen bonds without breaking, a slower relaxation (similar to 3.3ps) arising from the breaking dynamics of NMA(CO)-water hydrogen bonds, and another longer time constant (similar to 14 ps) aiming from the escape dynamics of water from the first hydration shell of carbonyl oxygen. The current results show that the NMA(CO)-water hydrogen bonds have a longer lifetime than those between water molecules, although frequency calculations reveal a slightly higher stretch frequency of the Water, molecules in the first hydration Shell of the carbonyl oxygen of NMA. An analysis of the vibrational spectral diffusion of solute modes is also presented in terms of the dynamics of solute-water hydrogen bonds. Effects of dispersion interactions On various calculated properties of the NMA-water system are also investigated in the present work.