Uncertain variables, such as electric power system parameters, have significant impacts on dynamic simulations of power systems. As traditional uncertainty analysis methods for power system dynamic simulations, both the simulation method and the approximation methods are difficult to balance the model complexity, computational efficiency, and simulation accuracy. In order to balance the model complexity, computational efficiency, and simulation accuracy, this paper proposes a method for uncertainty analysis for power system dynamic simulation based on the Nataf transformation and Gaussian-Hermite quadrature. Firstly, the samples on the normal distribution space are determined according to the Gaussian-Hermite quadrature points and the Nataf transformation. Secondly, obtain the simulation samples by inverse Nataf transformation, and perform power system dynamic simulation. Thirdly, the random output is approximated as a linear combination of a single random input, and the mean and standard deviation of the random output under the impact of a single random input are calculated by Gaussian-Hermite quadrature. Then, calculate the mean and standard deviation of the random output under the impact of all random input. Finally, the effectiveness of the proposed method is validated on the IEEE 9-bus system and IEEE 39-bus system. Compared with Monte Carlo simulation and Latin Hypercube sampling, the proposed method can greatly reduce the simulation time for uncertain dynamic simulations while maintaining high accuracy.