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The structural, electronic and optical properties of Cadmium Telluride (CdTe) are investigated at different pressures using the full potential linear muffin-tin orbital FP-LMTO method based on density functional theory (DFT), within the local density approximation LDA and the generalized gradient approximation GGA approximations were used to calculate  the exchange-correlation potential. The ground state properties of  CdTe compound were determined for diverse phases, and the band structure and optical parameters were calculated at pressures ranging from 0 GPa to 50 GPa. Optical parameters, including real part, imaginary part of the dielectric function, reflectivity, refractive index, extinction coefficient and energy loss function, were calculated for over an energy range from 0 eV to 13.6058 eV. The results were compared with available experimental and theoretical data, showing good agreement with earlier reported result. These particularities reveal that CdTe as favorable material for optoelectronic applications, as it exhibits together important electronic and optical responses under different pressure.