Undoped and Co-doped $ZnIn_2Se_4$ single crystals crystallized in the tetragonal space group 142m, with lattice constants a=5.748 $AA$ and c=11.475 $AA$, and a=5.567 $AA$ and c=11.401 $AA$. The optical absorption measured near the fundamental band edge showed that the optical energy band structure of these compounds had an indirect band gap, the direct and the indirect energy gaps of these compounds decreased as temperature changed from 10 to 300 K. The temperature coefficients of the direct energy gaps were found to be $alpha=3.71 imes10^{-4}$eV/K and $eta$=519 K for $alpha=3.71 imes10^{-4}$eV/K and $eta$=421K for $ZnIn_2Se_4$: Co. The temperature coefficients of the indirect energy gaps were also found to be $alpha=2.31 imes10^{-4}$ eV/K and $eta$=285 K for $ZnIn_2Se_4$, and $alpha=3.71 imes10^{-4}$eV/K and $eta$=609 K for $ZnIn_2Se_4$:Co, respectively. Six impurity optical absorption peaks due to cobalt are observed in $ZnIn_2Se_4$:Co single crystal. These impurity optical absorption peaks can be attibuted to the electronic transitions between the split energy levels of$CO^{2+}$ ions located at Td symmetry site of $ZnIn_2Se_4$ host lattice. The 1st order spin-orbit coupling constant ($lambda$), Racah parameter (B), and crystal field parameter (Dq) ARE GIVEN AS -$243 extrm{cm}^{-1}, 587 extrm{cm}^{-1}, ;and;327 extrm{cm}^{-1}$, respectively.