Temperature- and pressure-dependent studies of Raman and IR spectra have been performed on azetidinium zinc formate, [(CH2)3NH2][Zn(HCOO)3]. Vibrational spectra showed distinct anomalies in mode frequencies and bandwidths near 250 and 300 K, which were attributed to structural phase transitions associated with the gradual freezing of ring-puckering motions of the azetidinium cation. Pressure-dependent studies revealed a pressure-induced transition near 0.4 GPa. Raman spectra indicate that the structure of the room-temperature intermediate phase observed near 0.4 GPa is the same as the monoclinic structure observed at ambient pressure below 250 K. The second phase transition was found near 2.4 GPa. This transition has strong first-order character and is associated with strong distortion of both the zinc formate framework and azetidinium cations. The last phase transition was found near 7.0 GPa. This transition leads to lowering of the symmetry and further distortion of the zinc formate framework, whereas the azetidinium cation structure is weakly affected.