Abstract: To solve the problem of dynamic reliability of nuclear power plants under random ground motion excitation, a dynamic reliability analysis method was developed, with the extreme value distribution of the maximum response evaluated based on linear moments(L-moment). First, according to the target response spectrum, the corresponding time-history of ground motion samples were generated. Combined with the nuclear power structure finite element model, the time-domain explicit method was used in the random vibration analysis to obtain the node displacement response time-history sample. Then, the maximum displacement response time-history samples were estimated to determine the first three L-moment of the maximum response, and the three-parameter of maximum response distribution was determined according to the L-moment matching. Finally, based on the maximum response distribution, the reliability under different thresholds was estimated. Results show that when the peak value of seismic acceleration is 0.3 g, the containment structure has good reliability with slight damage as the boundary, and still has certain reliability with medium damage. The dynamic reliability analysis of the nuclear power plant shows that compared with the Monte Carlo method, this method greatly reduces the minimum sample size and improves the computational efficiency of the simulated tail while ensuring the calculation accuracy. At the same time, it has wide applicability for solving the problem of dynamic reliability of other structures.