Zn$_4$SnSe$_{6}$ and Zn$_4$SnSe$_{6}$ :Co$^{2+}$ single crystals were by the chemical transport reaction method. They crystallized in the monoclinic structure. The direct energy band gaps of the Zn$_4$SnSe$_{6}$ and Zn$_4$SnSe$_{6}$ :Co$^{2+}$single crystals at 289k were found to be 2.146eV and 2.042eV. Optical absorption due to impurity in the Zn$_4$SnSe$_{6}$ :Co$^{2+}$single crystal was observed and described as originating from the electron transition between energy levels of Co$^{2+}$ion sited at T$_{d}$ symmetry point.y point.