The growth of the AlGaSbInAs high-electron-mobility transistor (HEMT) epitaxial structure on the Si substrate is investigated. Buffer layers consisted of UHV/chemical vapor deposited grown GeGeSi and molecular beam epitaxy-grown AlGaSbAlSbGaAs were used to accommodate the strain induced by the large lattice mismatch between the AlGaSbInAs 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 AlGaSbInAs HEMT structure on the Si substrate can be achieved with the properly designed buffer layers.