We report the epitaxial growth of MgO and CoFe/MgO on Ge (001) substrates using molecular beam epitaxy. It wits found that the epitaxial growth of a MgO film on Ge Could be realized at a low growth temperature of 125 +/- 5 degrees C and the MgO matches the Ge with a cell ratio of 2(1/2):1, which renders MgO rotated by 45 degrees relative to Ge. In-situ and ex-situ structural characterizations reveal the epitaxial crystal growth of bee CoFe/MgO on Ge with the in-plane crystallographic relationship of CoFe(001)[100](parallel to)MgO(001)[110](parallel to)Ge(001)[100], exhibiting sharp interfaces in the (001) matching planes. The saturation magnetization of the sample is 1430 +/- 20 emu/cc, which is comparable to the value of bulk CoFe.