The cooperativity between the O-H center dot center dot center dot O and C-H center dot center dot center dot O hydrogen bonds has been studied by quantum chemical calculations at the MP2/6-311++G(d,p) level in gaseous phase and at the B3LYP/6-311++G(d,p) level in solution. The interaction energies of the O-H center dot center dot center dot O and C-H center dot center dot center dot O H-bonds are increased by 53 and 58%, respectively, demonstrating that there is a large cooperativity. Analysis of hydrogen -bonding lengths, OH bond lengths, and OH stretching frequencies also supports such a conclusion. By NBO analysis, it is found that orbital interaction plays a great role in enhancing their cooperativity. The strength increase of the C-H center dot center dot center dot O H-bond is larger than that of the O-H center dot center dot center dot O H-bond due to the cooperativity. The solvent has a weakening effect on the cooperativity.