HgGa$_2$S$_4$: Co$^{2＋}$ single crystal were grown by the chemical transport reaction(CTR) method. In the optical absorption spectrum of the HgGa$_2$S$_4$: Co$^{2＋}$ single crystal measured at 298K, three groups of impurity optical absorption peaks consisting of three peaks, respectively, were observed at 673nm, 734nm, and 760nm, 1621nm, 1654nm, and 1734nm, and 2544nm, 2650nm, and 2678nm. At 10K, the three peaks(673nm, 734nm, and 760nm) of the first group were split to be twelve peaks. These impurity optical absolution peaks are assigned to be due to the electronic transitions between the split energy levels of Co$^{2＋}$ sited in the S$_4$ symmetry point.