We report a detailed experimental investigation of Raman phonon spectra of crystals of 1,4-diiodobenzene (p-DIB) in the pressure range 0-7.5 GPa. Strong modifications of spectral profiles as a function of pressure suggest the possibility of two pressure-induced phase transitions at 0.4 and 1.7 GPa. Quasi-harmonic lattice dynamics (QHLD) calculations, based on intermolecular atom-atom potentials, are applied to model the ambient p,T crystal structure and the pressure dependence of the Raman-active lattice phonons.