Time-resolved radiative recombination measurements on GaSb quantum dots have been performed. The GaSb quantum dots are grown by molecular beam epitaxy on ͑100͒ GaAs through a self-assembly process. Time-resolved measurements show that, after a rapid hole capture process, the photoluminescence decays with a fast and a slow component. The fast component is shortened significantly with higher excitation intensity while the slow component is roughly constant. The radiative lifetimes are much longer than the lifetimes of ordinary GaSb quantum wells with a straddling band lineup. These results support a staggered band lineup and space charge induced band-bending model.