As a high-k oxide in a perovskite structure, LaAlO3 undergoes a rhombohedral-to-cubic structural phase transition under high pressure. Such phase transition is characterized as a continuous phase transition. In order to study the pressure effect, we use the first principle density functional perturbation theory to calculate the total energies with respect to various pressures in this thesis, and also analyze the corresponding lattice dynamics properties. Based on the Landau theory, calculated phonon frequency of LaAlO3 in different structural symmetries indicates a typical pressure-induced mode softening effect. Moreover, the pressure effects on Raman intensity and the deformation potential is also discussed in this work.