Full-Heusler alloy Co2MnGe thin films were epitaxially grown on MgO (001) substrates using magnetron sputtering. The films were deposited at room temperature and subsequently annealed in situ at temperatures ranging from 400 to 600 degrees C. X-ray pole figure measurements for the annealed films showed (111) peaks with fourfold symmetry, which gives direct evidence that these films are epitaxial and crystallized in the L2(1) structure. Furthermore, cross-sectional transmission electron microscope images of a fabricated film indicated that it is single crystalline. The annealed films had sufficiently flat surface morphologies with roughnesses of about 0.26 nm rms at film thicknesses of 45 nm. The saturation magnetization of the annealed films was 4.49 mu(B)/f.u. at 10 K, corresponding to about 90% of the Slater-Pauling value for Co2MnGe.