This paper aims to investigate the stochastic resonance(SR) in an Fitz Hugh-Nagumo(FHN) model with an additive Lévy noise numerically. The non-Gaussian Lévy noise is a kind of general random noise which is different from the usual Gaussian noise, and it has small fluctuations with the unpredictable jumps to describe the random fluctuations in an FHN model. SR is determined by the signal-to-noise ratio(SNR), and the numerical simulation results show the occurrence of the SR phenomena in the given FHN system. The influence of various parameters of the Lévy noise and the FHN model on the SR will be examined, and some mechanisms of the Lévy noise-induced SR are presented which are different from those of the Gaussian noise. This non-Gaussian Lévy noise is a kind of general random noise which is different from the usual Gaussian noise, and it has small fluctuations with the unpredictable jumps to describe the random fluctuations in an FHN model. SR is determined by the signal-to-noise ratio (SNR), and the numerical simulation results show the occurrence of the SR phenomena in the given FHN system. The influence of various parameters of the Lévy noise and the FHN model on the SR will be examined, and some mechanisms of the Lévy noise-induced SR are presented which are different from those of the Gaussian noise.