We investigated the FitzHugh-Nagumo neural system driven by non-Gaussian noise. The expressions of the stationary probability distribution and the mean first-passage time are obtained through the path-integral approach and the unified colored noise approximation. The results show that the intensity of additive noise can induce phase transition，while the intensity of multiplicative noise，the derivation parameter and the correlation time cannot. The non-Gaussian noise shortens transformation time between resting state and excited state and is beneficial to transmission of information in neural system.