We report on the epitaxial growth of high electron mobility AlSb/InAs heterostructure on exactly oriented (001) Si substrate, using a GaP interfacial layer. The growth conditions are first optimized on GaP substrates to achieve the highest electron mobility. The influence of the Sb flux during the early stage of the GaSb buffer layer is particularly emphasized. Using these optimized growth conditions, the AlSb/InAs heterostructure is grown on a GaP/Si template obtained by metal-organic vapor phase epitaxy. An electron mobility as high as 27 800 cm2 V−1 s−1 and 111 000 cm2 V−1 s−1, respectively, at 300 and 77 K is demonstrated.