A structure of high electron mobility transistor growth on Si substrate and the method thereof, in particular used for the semiconductor device manufacturing in the semiconductor industry. The UHVCVD system was used in the related invention to grow a Ge film on Si substrate then grow the high electron mobility transistor on the Ge film for the reduction of buffer layer thickness and cost. The function of the Ge film is preventing the formation of silicon oxide when growing III-V MHEMT structure in MOCVD system on Si substrate. The reason of using MHEMT in the invention is that the metamorphic buffer layer in MHEMT structure could block the penetration of dislocation which is formed because of the very large lattice mismatch (4.2%) between Ge and Si substrate.