Twelve glycine-H2O2 complexes are studied at the density three-parameter hybrid functional DFT-B3LYP/ 6-31 ++G(d,p) level regarding their geometries, energies, vibrational frequencies, and topological features of the electron density. Natural bond orbital (NBO) analysis and the Bader's theory of atoms in molecules (AIM) are employed to elucidate the interaction characteristics in the complexes. These complexes except for III-1 are doubly hydrogen bonding. The distinct cooperative effect and the typical resonance-assisted hydrogen-bonding mechanism are exhibited in the six-membered rings of complexes I-1 and II-1. The binding energies play a central role in the relative stabilities of the complexes, among which I-1 is the most stable conformer. A strength sequence of the hydrogen bonds from the strongest to the weakest is found: O-H...N, O-H...O, N-H...O, and C-H...O. The blue- and red-shifts in the local X-H (X = O, C, N) stretching frequencies are proportional to the bond elongations or shortening lengths. The NBO analyses show that the electronic charge is transferred from glycine to H2O2 in these complexes except for I-1 and II-1. The electron density p at the hydrogen bond critical point predicted by AIM is strongly correlated with the hydrogen bond parameter deltaR(H...Y) (the difference between the sum of the van der Waals radii of H and Y atoms and the length of hydrogen bond H...Y), the Fock matrix element F-ij in the NBO scheme, and the interaction energy of the complex.