Spin field effect transistor, an essential building block for spin information processing, shows promise for energy-efficient computing. Despite steady progress, it suffers from a low output signal because of low spin injection and detection efficiencies. We demonstrate that this low-output obstacle can be overcome by utilizing direct and inverse spin Hall effects for spin injection and detection, respectively, without a ferromagnetic component. The output voltage of our all-electric spin Hall transistor is about two orders of magnitude larger than previously reported spin transistors based on ferromagnets or quantum point-contacts. Moreover, the symmetry of spin Hall effect allows all-electric spin Hall transistors to effectively mimic n-type and p-type devices, opening a way of realizing the complementary functionality.