The growth of the AlGaSb/InAs high-electron-mobility transistor (HEMT) epitaxial structure on the Si substrate is investigated. Buffer layers consisted of UHV/chemical vapor deposited grown Ge/GeSi and molecular beam epitaxy-grown AlGaSb/AlSb/GaAs were used to accommodate the strain induced by the large lattice mismatch between the AlGaSb/InAs HEMT structure and the Si substrate. The crystalline quality of the structure grown was examined by x-ray diffraction, transmission electron microscopy, and atomic force microscopy. Finally, very high room-temperature electron mobility of 27 300 cm2/V s was achieved. It is demonstrated that a very-high-mobility AlGaSb/InAs HEMT structure on the Si substrate can be achieved with the properly designed buffer layers.