As a new generation of reactor type, lead-cooled fast reactors, have better safety behaviors, higher reliability, and better economic performance, aiming at island power supply through nuclear energy, seawater desalination, optimization of nuclear submarines, etc. Its evolution of nuclear waste and the advantages of nuclear non-proliferation provide a good prospect for development. This paper studied the safety performances of an offshore stationary lead-cooled reactor (OSLR) proposed in the National Key Research and Development Program of China. The transient analysis code SAS4A/SASSYS-1 was used to perform simulations of unprotected over-power accidents (UTOP) and unprotected loss of heat sink (ULOHS) accidents. The results indicated that offshore stationary lead-cooled reactors can withstand a maximum positive reactivity insertion of 0.5$ within 1 s during UTOP accidents without exceeding the working limits of the core. In ULOHS accidents, the inherent safety characteristics of OSLR allowed it to withstand 75 % heat removal capability of IHX. The simulation results were used to analyze the response of this stationary offshore reactor to transient accident conditions and the limits of its ability to withstand accidents in order to provide reference data for subsequent design and ideas for possible development of natural cycle lead-cooled reactors in the future.