alpha-Glycylglycine in its actual crystalline phase is studied by ab initio calculated nuclear quadrupole coupling constants. These physical quantities are computed for H-2 and N-14 in the hydrogen bonds. The type of hydrogen bond is the N-(HO)-O-... type. The computations are performed with the RHF and B3LYP methods and 6-31++G** and 6-311++G** basis sets using the Gaussian 98 program. Values of the calculated nuclear quadrupole coupling constants are shown in Tables 1-3. The aim of this work is the study of 2H and 14N quadrupole coupling constants which contribute in the (CONHO)-H-2-O-...=(CNH)-H-2 type of hydrogen bond. The computed nuclear quadrupole coupling constants of H-2 nuclei meet the related experimental values. In addition, the computed chi value of N-14 belonging to the -CO-(NH)-N-14- group agrees well with values obtained experimentally. However, there are some discrepancies between calculated N-14 chi values of the N+H3 residue and experiments. Also, the values of these physical parameters are calculated for >(CH2)-H-2 of alpha-glycylglycine in its crystalline phase. Calculations for these parameters are carried out in a single molecule using X-ray diffraction coordinates, too.