The role of hydrogen bonds in energy redistribution in the cyclic structure of a formamide-water complex has been studied with semiclassical formulations of energy transfer probabilities and solutions of the equations of motion. We show high efficiency of near-resonant vibrational energy from initially excited OH stretching to the first overtone of the bending vibration, which is followed by ultrafast (similar to 100 fs) energy redistribution in the accepting modes of the complex. A strong coupling of the OH bending vibration with the low-frequency modes generated in the hydrogen-bonding intermolecular regions, especially that formed between the water oxygen and formamide hydrogen, plays the key role of ultrafast relaxation of the overtone mode, transferring energy to the hydrogen bonds and distant functional groups in the complex.