Two models of a designed small size lead-cooled fast reactor (LFR) were built by RELAP5-HD to simulate the behavior of the reactor system during pump shutdown accidents, along with different levels of core blockage. Two typical pump shutdown accidents of pump rotor seizure accident and loss-of-pump-power accident were selected to do the simulation and analysis of the behavior of the nuclear power reactor during pump shutdown accidents, when all the safety systems were assumed to be unavailable. A one dimensional vessel-one dimensional core model was built to simulate the long term cooling condition of the pump shutdown accidents under the reactor shutdown or operation conditions. The simulation results would help to analyze whether pump accidents could cause core damage. In order to show the heat removing capability of the coolant in the reactor system, a more detailed one dimensional vessel-three dimensional core model was built to simulate the long term cooling condition of the pump shutdown accidents along with different levels of core blockage accidents.