The purpose of this study is to modify all physicochemical properties of glycine–copper sulphate single crystals, such as crystal habits, molar mass, thermal stability, optical activity, and electrical properties. The novelty of this study is growth of glycine–copper sulphate single crystals doped by a low concentration of silver nanoparticles (SNPs) that improved both crystal habits and physicochemical properties. The originality of this work is that trace amounts of SNPs largely increased the crystal size. Crystals have molar stoichiometric formula [glycine]0.95, [CuSO4·5H2O]0.05 in the absence and presence of silver nanoparticles (SNPs) in different concentrations: 10 ppm, 20 ppm, and 30 ppm. The crystals’ names and abbreviations are: glycine–copper sulphate (GCS), glycine–copper sulphate doped by 10 ppm SNPs (GCSN1), glycine–copper sulphate doped by 20 ppm SNPs (GCSN2), and glycine–copper sulphate doped by 30 ppm SNPs (GCSN3). Dopant silver nanoparticles increased: crystallinity reflecting purity, transparency to UV-Vis. electromagnetic radiation, thermal stability, and melting point of glycine–copper sulphate single crystal. GCSN3 is a super conductor. High thermal conductivity of crystals ranging from 1.1 W·min−1·K−1 to 1.6 W·min−1·K−1 enabled attenuation of electromagnetic radiation and rapid heat dissipation due to good dielectric and polar properties. On rising temperature, AC electrical conductivity and dielectric properties of perfect crystal GCSN3 increased confirmed attenuation of thermal infrared radiation.