By means of monitoring with the reflection high energy electron diffraction (RHEED) -and its intensity oscillations, the GaSb/AlSb/GaAs strained layer heterostructures have been suc-cessfully grown on semi-insulating (100) GaAs substrates by molecular beam epitaxy (MBE) The RHEED patterns show that the GaSb surface grown under Sb-stabilized condition has C (2×6) structure and the AlSb surface has (1×3) Sb structure. We observed and recorded the RHEED intensity oscillations during the growth of GaSb and AlSb. Using the information provided by the RHEED intensity oscillations, we successfully prepared a GaSb/AlSb super-lattice with 10 periods. The transmission electron micrograph shows the interfaces in the su-perlattice are sharp and planar. If the AlSb buffer layer is thick enough under a proper growth condition, a high-quality GaSb epitaxy will be grown on SI GaAs substrate. The full width at half maximun (FWHM) of the peak corresponding to the GaSb epilayer in double-crystal X-ray diffraction rocking curve is less than 300 seconds. Undoped GaSb is p-type with carrier concentration of 2.12×1016 cm-3 and mobility of 664cm2/V·s at room temperature.