The single crystals of $Mg_{0.15}Zn_{0.85}Te$ and $Mg_{0.15}Zn_{0.85}Te:Co^{2+}$(0.001%) were grown by vertical Bridgman method. Optical absorption properties of this compound were studied. As a result of the optical absorption spectra of $Mg_{0.15}Zn_{0.85}Te$, absorption peaks were related to exciton and the exciton level redshifts with increasing temperature, and temperature coefficient given to the value of $-5.8{ imes}10^{-4};eV/K$ for the temperature range above 100 K. in the $Mg_{0.15}Zn_{0.85}Te:Co^{2+}$(0.001%) single crystal, the intracenter transitions due to $Co^{2+}$ ions were detected for $A-band:^4A_2(^4F) { o}^4T_1(^4F),; B-band:; ^4A_2(^4F){ o}^4T_1(^4P)$, and the charge transfer transition near the absorption edge was observed in the wavelength range of 500 to 800 nm. According to the crystal field theory and Lucovsky formula, the crystal field parameter, Racah parameter and charge transfer energy were determined.