We prepared GaSb/AlGaSb multi-quantum-well (MQW) structures on n-type silicon (001) substrates by molecular beam epitaxy (MBE). To minimize dislocations in MQW layers and decrease the total thickness of the epitaxial layer, we employed not only an AlSb initiation layer but also a superlattice buffer layer (SL-BL) in a moderately thick GaSb buffer layer. For comparison we also fabricated other MQW structures on a considerably thick GaSb buffer layer without SL-BL. The obtained atomic force microscopy (AFM), transmission electron microscopy (TEM) images and high-resolution X-ray diffraction (XRD) patterns indicated that the definite MQW structures for both the samples and the quality of MQW layers prepared using SL-BL were generally better than those of the reference sample. The PL emission of these samples at about 1.30 -1.55 mm was observed at room and low temperatures. The dependence of PL emission energy on GaSb well width was well explained by the finite square well potential model.