In nanomaterials, optical anisotropies reveal a fundamental relationship between structural and optical properties, in which directional optical properties can be exploited to enhance the performance of optoelectronic devices. First principles calculation based on density functional theory (DFT) with the generalized gradient approximation (GGA) are carried out to investigate the energy band gap structure on silicon (Si) and germanium (Ge) nanofilms. Simulation results show that the band gaps in Si (100) and Ge (111) nanofilms become the direct-gap structure in the thickness range less than 7.64 nm and 7.25 nm respectively, but the band gaps of Si (111) and Ge (110) nanofilms still keep in an indirect-gap structure and are independent on film thickness, and the band gaps of Si (110) and Ge (100) nanofilms could be transferred into the direct-gap structure in nanofilms with smaller thickness. It is amazing that the band gaps of Si(1-x)/(GeSi(1-x)/2)-Ge-2-Si-x sandwich structure become the direct-gap structure in a certain area whether (111) or (100) surface. The band structure change of Si and Ge thin films in three orientations is not the same and the physical mechanism is very interesting, where the changes of the band gaps on the Si and Ge nanofilms follow the quantum confinement effects.