Epitaxial BaTiO3 (BTO) thin films were deposited by molecular beam epitaxy on (001) silicon using an approximately 5 ML thick SrTiO3 (STO) as an intermediate buffer layer. In situ reflection high-energy electron diffraction (RHEED) was employed to quantitatively determine strain relaxation from the change in the in-plane lattice spacing. The crystalline quality, composition, and surface morphology of the BTO thin films were characterized by a combination of x-ray diffraction (XRD), atomic force microscopy, and x-ray photoelectron spectroscopy. RHEED analysis indicates that the initial growth of BTO was pseudomorphic. Strain relaxation occurred when the thickness reached a critical value of 10 MLs or 4nm. The lattice spacing approached the bulk BTO value for films with 30nm thickness. The BTO layer grows via a two dimensional growth mode. XRD measurement indicates a rocking curving width of the BTO (002) peak on Si as low as 0.9° has been achieved. Strain relaxation of the BTO films grown on different substrates including MgO, MgO/STO buffered Si, and STO buffered Si are compared.