We report in situ high-pressure Raman spectroscopic as well as X-ray diffraction measurements on bis(glycinium)oxalate, an organic complex of glycine, up to 35 GPa. Several spectral features indicate that at similar to 1.7 GPa it transforms to a new structure (phase II) which is characterized by the loss of the center of symmetry and the existence of two nonidentical glycine molecules. Across the transition, all the N-H center dot center dot center dot O bonds are broken and new weaker N-H center dot center dot center dot O bonds are formed. Our high-pressure X-ray diffraction studies support the possibility of a non-centrosymmetric space group P2(1) for phase II. Across 5 GPa, another reorganization of N-H center dot center dot center dot O hydrogen bonds takes place along with a structural transformation to phase III. The C-C stretching mode of oxalate shows pressure-induced softening with large reduction from the initial value of 856 to 820 cm(-1) up to 18 GPa, and further softening is hindered at higher pressures.