The pressure-induced phase transformations in pure LiAlH4 have been studied using in situ Raman spectroscopy up to 7 GPa. The analyses of Raman spectra reveal a phase transition at approximately 3 GPa from the ambient pressure monoclinic alpha-LiAlH4 phase (P2(1)/c) to a high pressure phase (beta-LiAlH4, reported recently to be monoclinic with space group I4(1)/b) having a distorted [AlH4](-) tetrahedron. The Al-H stretching mode softens and shifts dramatically to lower frequencies beyond the phase transformation pressure. The high pressure,- LiAlH4 phase was pressure quenchable and can be recovered at lower pressures (similar to 1.2 GPa). The Al-H stretching mode in the quenched state further shifts to lower frequencies, suggesting a weakening of the Al-H bond.