In this paper, we report on the TL glow curves and kinetic parameters, activation energy, order of kinetics, and the frequency factor of copper-doped zinc sulfide nanophosphor under UV irradiations. The sample was prepared by the chemical precipitation method; thereafter, the TL glow curves were recorded for different doses of UV exposure at a heating rate of 10 °C/s. The synthesized nanophosphor exhibited TL glow peaks at 241, 255, and 281 °C for the heating rate 10 °C/s at different doses of 5, 10, and 15 min of UV exposure. The kinetic parameters activation energy E, the order of kinetics b, and the frequency factor S of synthesized nanophosphor of ZnS:Cu have been calculated by using a peak shape method while the trap depth was determined using different formulae. The sample was characterized by XRD (X-ray diffraction) and SEM (scanning electron microscope).