This work reports on the epitaxial growth of crystalline high-k Gd2O3 on Si (111) by Molecular Beam Epitaxy (MBE) for CMOS gate application. Epitaxial Gd2O3 films of different thicknesses have been deposited on Si (111) between 650°C~750°C. Electrical characterizations reveal that the sample grown at the optimal temperature (700°C) presents an equivalent oxide thickness (EOT) of 0.73nm with a leakage current density of 3.6×10-2 A/cm2 at |Vg-VFB|=1V. Different Post deposition Annealing (PDA) treatments have been performed for the samples grown under optimal condition. The Gd2O3 films exhibit good stability and the PDA process can effectively reduce the defect density in the oxide layer, which results in higher performances of the Gd2O3/Si (111) capacitor.