After a nuclear power plant accident, analyzing, predicting, and evaluating the concentrations of radionuclides at various distances from the nuclear power plant site and assessing the doses and risks to personnel, are essential components of Level 3 Probabilistic Safety Analysis (PSA) for nuclear power plants. Accurate and rapid consideration of radionuclide decay, as well as reliable calculation of radionuclide concentration fields around the nuclear power plant, is a key step to Level 3 PSA. Traditional methods for calculating radionuclide decay generally only consider the situation of three generation progenies. However, given that dose and risk calculations need to account for hourly meteorological conditions for several tens of hours, it is necessary to consider the complete decay chain as much as possible, and the calculation time for nuclide decay should not be too long. Based on the differential equations of radioactive decay chains, this paper utilizes matrix analysis to calculate the decay of radioactive nuclides. Taking the radioactive nuclide concentration of Level 3 PSA of a nuclear power plant as an example, the calculation results are provided and the calculation time is only a few seconds. This approach provides an optimized and efficient methodology for Level 3 PSA of nuclear power plants.