$CdIn_2S_4 and CdIn_2S_4 : Co^{2+}$ singlecrystals of thenormal spinel structure were grown by the C.T.R. method. The optical energy band structure of these compounds had a indirect band gap at the fundamental optical absorption band edge. The direct and the indirect energy gaps are found to be 2.325 and2.179eV for $Cdln_2S_4$ , and 2.303 and 2.169eV for $CdIn_2S_4 and CdIn_2S_4 : Co^{2+}$ at 5K, respectivly. The fundamental absorption band edge of these single crystals shift to a shorter wavelength region with decreasing temperature, and the temperature dependence of the optical energy gaps in these compounds satisfy Varshni equation. The Varshni constants$alpha and eta$ of the direct energy gap are given by $13.39{ imes}10_{-4}eV/K$ and 509 K for $Cdln_2S_4$ and $29.73{ imes}10_{-4} eV/K$ and 1398K for $CdIn_2S_4 and CdIn_2S_4 : Co^{2+}$. The Varshni constants ${alpha}and {eta}$ of the indirect energy gap are given by 9.68${ imes}10^{-4}$ eV/K 308K for $Cdln_2S_4$ and $13.33{ imes}10_{-4}eV/K$ and 440K for $CdIn_2S_4 : Co^{2+}$ respectivly. The impurity optical absorption peaks due to cobalt dopant are observed in $CdIn_2S_4 : Co^{2+}$ single crystal. These impurity optical absorption peaks can be attributed to the electronic transitions between the split energy levels of $Co_{2+}$ ions located at $T_d$ symmetry site of $Cdln_2S_4$ host lattece.