Even though the noise model applied in power system dynamic state estimation (DSE) is usually assumed to be Gaussian, this is not the case due to the unknown system inputs, influence from the communication channel noise, and the outliers generated by phasor measurement units (PMUs). In this article, a robust power system DSE method combining a robust exponential-absolute-value-based estimator and the unscented Kalman filter (UKF) together is proposed under non-Gaussian noise. Based on the quadratic function and the exponential absolute value function, robust exponential-absolute-value-based estimator is derived, further mitigating the effects of bad data or outliers. The influence function is used to calculate the state estimation error covariance of the proposed robust DSE method. The simulation results on the IEEE 39-bus system verify the robustness and effectiveness of the proposed DSE method.