Improvement of power supply security is of paramount importance to sustain human activities. Technical and engineering failures of power grid system have been analyzed to evaluate power system reliability hitherto. However, after Fukushima nuclear accident, the sudden electricity supply disruption particularly associated with nuclear energy utilization brings upon a new risk of electricity supply security arising from societal issues, or nuclear vulnerability. As such, a methodology of quantifying nuclear vulnerability is firstly established under varying both the magnitude and time instant of sudden stoppage of nuclear power operation. Through the nuclear vulnerability analysis, a new electricity supply security index dedicated for nuclear power utilization, named System Interruption Nuclear Vulnerability Index (SINVI) is developed. SINVI could be used to predict the risk of electricity supply disruption arising from the sudden stoppage of nuclear power operation corresponding to the different capacity combination of various energy sources. Finally, the widely proposed dimensions of energy security for undisturbed electricity supply diversification and redundancy are incorporated with nuclear vulnerability to design the more secured power system taking into account the risk of nuclear energy utilization. The established algorithm can be readily implemented in any other electricity grid network including nuclear power technology.