Optical properties of $Ag_2CdSnSe_4$ and $Ag_2CdSnSe_4:Co^{+2}$ quaternary semiconductor single crystals grown by the chemical transport reaction method were investigated. The analysis of the X - ray powder diffraction measurements showed that these crystals have a wurtzite structure with lattice constants a = 4.357 $AA$, c = 7.380 $AA$, for $Ag_2CdSnSe_4$ and a = 4.885 $AA$, c = 7.374 $AA$, for $Ag_2CdSnSe_4:CO^{2+}$. The direct band gap at 298K, obtained from the optical absorption measurement, is found to be 1.21 eV for $Ag_2CdSnSe_4$ and 1.02 eV for $Ag_2CdSnSe_4:CO^{2+}$. The shrinkage of the band gap due to Co-doping is observed and is about 190 meV, We observed four absorption bands of $Co^{2+}$ ions in two near infrared regions of optical absorption spectra of $Ag_2CdSnSe_4$:$Co^{+2}$. These absorption bands were assigned as due to electronic transitions between the split energy levels of $Co^{2+}$ ions in $T_d$ crystal field under spin-orbit interactions.