We have successfully fabricated foreign-catalyst-free GaSb nanowires directly on cleaved Si (111) substrates by molecular-beam epitaxy. We find that GaSb nanowires with the absence and presence of Ga droplets at the tip can be simultaneously obtained on cleaved Si substrates without Ga pre-deposition. Systematic morphological and structural studies verify that the two kinds of nanowires presented have different growth mechanisms, which are vapor-solid and vapor-liquid-solid mechanisms. The growth of GaSb nanowires can also be achieved on cleaved Si (110) and Si (100) substrates. The cleavage plane of the Si substrate has an obvious influence on the growth of the GaSb nanowires. The growth direction and crystal quality of catalyst-free nanowires are independent of the cleavage plane of the substrate. Our results may facilitate the understanding of the growth mechanism of III-V nanowires and the integration of foreign-catalyst-free GaSb nanowire-based devices with mature semiconductor technology.