Bio-preservative agents such as trehalose and glycerol are commonly used to preserve biomolecules against denaturation and its consequent loss of activity. The molecular mechanisms that control the preservation ability of such bio-protective agents is not fully understood at present. Studies of the fast dynamic behavior of these agents, which is a consequence of the small-amplitude atomistic motions in the system, provide valuable information in understanding this phenomena. We present a molecular dynamics simulation study of the fast dynamics of trehalose-glycerol mixtures with different compositions and at different temperatures. We found that a mixture of five percent glycerol (a liquid) and ninety five percent trehalose (a fragile glass) is the most efficient one in suppressing the short time local dynamics of the trehalose molecules. We link this counter-intuitive finding to our observation that at this composition the mixture is networked by a more robust hydrogen bonding structure as compared to other compositions. Comparisons between our simulation results and data from neutron scattering experiments will be discussed.