The variation of pressure is an effective experimental technique to explore new polymorphs of organic crystals. At ambient condition, oxalyl dihydrazide (C2N4O2H6, ODH) exhibits five polymorphs: alpha, beta, delta, gamma, and epsilon. Here we report the high-pressure response of the existed five forms of ODH by in situ Raman spectroscopy and synchrotron X-ray diffraction techniques with a pressure of about 20 GPa. High-pressure experimental results show that all five polymorphs undergo phase transitions to new phases at different pressures, respectively. We propose that the special molecular conformation yields several geometric constructions for hydrogen-bonding arrangements. The detailed mechanisms of the phase transition and the high-pressure behaviors of the polymorphs are analyzed by considering molecular stacking.