The behavior of the crystal structure of the zeolitic imidazolate framework ZIF-75 under pressure was studied by means of periodic density functional theory methods. Experimentally, it was shown that this material is tetragonal, space group , at room temperature. However, according to the calculations, at zero temperature this material is monoclinic, space group . Irrespective of the symmetry of the material, the results show that ZIF-75 exhibits a negative linear compressibility effect and is unstable under relatively small applied pressures of the order of 0.1 GPa.