We demonstrate the formation of GaSb quantum dots (QDs) on a GaAs(001) substrate by droplet epitaxy using molecular beam epitaxy. The high crystal quality and bimodal size distribution of the QDs are confirmed using atomic force and transmission electron microscope images. A staggered type-II QD band structure is suggested by a photoluminescence peak that is blue shifted with increasing excitation intensity, a large emission polarization of 60%, and a long carrier decay time of 11.5 ns. Our research provides a different approach to fabricating high quality GaSb type-II QDs.