In this study, the shutdown system of the fuel gas supply system is designed based on the Safety Integrity Level of IEC 61508 and IEC 61511. First of all, the individual risk($10^{-4}$/year) and the risk matrix which are the risk acceptance criteria are set up for the qualitative risk assessment such as the HAZOP study. The natural gas leakage at the gas supply pipe is identified as the highest risk among the hazards identified through the HAZOP study and as a safety instrumented function the shutdown function for leakage was defined. SIL 2 and PFD($2.5{cdot}10^{-3}$) for the shutdown function are determined by the layer of protection analysis(LOPA). The shutdown system(SIS) carrying out the shutdown function(SIF) is verified and designed according to qualitative and quantitative requirements of IEC 61508 and IEC 61511. As a result of SIL verification and SIS conceptual design, the shutdown system is composed of two gas detectors voted 1oo2, one programmable logic solver, and two shutdown valve voted 1oo2.