In-situ organization of InSb quantum dots on Al0.5Ga0.5Sb is reported. Samples were grown on just (100), 5°off (100) towards [0-1-1],(311)A, and (311)B surfaces of GaAs by molecular beam epitaxy. The growth mechanism and characteristics of quantum dots were analyzed using reflection high-energy electron diffraction, atomic force microscopy, and photoluminescence. Observed photoluminescence peak shift towards lower energy side with InSb thickness was interpreted by the development of quantum dots. Substrate orientation effect was examined and found to be useful to increase the dot density. As a result, as high as ~3xl 09 cm-2 dot density was achieved on the (311 )B substrate whereas the typical value on the (100) was ~2xl 08 cm-2 .