Abstract: Based on analysis of the production mechanism of fission products in the nuclear component without exterior neutron radiation and the delayed γ-rays released from the products, a simulation method for calculating the fission product activities and their variations with time was proposed using CINDER90 program. According to energy and branch ratios of the delayed γ-rays released from β^- decay of the fission products, the intensities of the different γ-rays were calculated. Then, the variations of the delayed γ-ray spectra of the nuclear component with radiation time and cooling time were calculated by Monte Carlo method, and the time evolution behaviors of the delayed γ-ray spectra were analyzed. The results show that the maximum intensity ray in the delayed γ spectra from nuclear component is released from ¹⁴⁰La β^- decay, the γ-ray energy is 1596 keV, and its intensity remains stable after the component is assembled for a certain time. These results agree well with the ones in the literature. The simulation method and the calculation results presented in this paper can be used as a reference for the spectrum measurement and analysis of nuclear components.