HgGa$_2$S$_4$ single crystals were grown by the chemical transport reaction method. The HgGa$_2$S$_4$ single crystal crystallized into a defect chalcopyrite structure (I 4). The lattice constants of the single crystal were found to be a = 5.635 $AA$ and c = 10.473 $AA$. The direct and indirect optical energy gaps were found to be 2.84eV and 2.78eV, respectively. Photoluminescence peaks of HgGa$_2$S$_4$ single crystal were observed at 2.37 eV, 2.18 eV, and 1.81 eV. In the single crystal, the donor level of 0.25 eV, the acceptor levels of 0.97 eV and 0.41 eV were obtained by TSC, PICTS, and absorption measurements. The photoluminescence peaks were analyzed to relate to the indirect conduction band, the donor level, and the acceptor levels.?????1????L????