Glycine zinc sulfate (GZS) single crystals pure and doped with copper were grown by the slow evaporation of aqueous solutions at constant temperature (307 K). Cu/Zn molar ratios were 1%, 2% and 3% in the growth solutions. The optical reflectance was measured for pure and doped crystals (GZS:Cu) and it was used to calculate several optical and dielectric parameters. The direct optical band gap energy was found to be 5.44 eV for pure GZS crystal and it decreased as Cu/Zn molar ratio increased. The band tailing was studied for GZS:Cu crystals by using Urbach relation. The normal dispersion was investigated for GZS:Cu crystals by using both Wemplee–Di-Domenico and Cauchy-Sellmaier models. The real and imaginary parts of the complex dielectric constant of GZS:Cu crystals were calculated. Urbach parameters, normal dispersion parameters and dielectric parameters of GZS:Cu crystals were calculated in the present work for the first time. It was found that doping GZS crystal, with copper, affects the values of its optical and dielectric parameters and improves its electrical conduction.