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This paper mainly studies the phenomenon of inverse stochastic resonance induced by non-Gaussian noise in a representative Hodgkin–Huxley model. Firstly, spiking manners of neurons under different input currents are investigated and different current thresholds and bifurcation diagram are given. Besides, the limit cycle with different input current are plotted. Then, taking the average firing rate as a measurement, the result shows that a minimum exists in the curve corresponding to the intensity, correlation time and deviation coefficient of non-Gaussian noise, which is named inverse stochastic resonance(ISR). More important, it is found that the mean firing rate will remain unchanged with noise intensity and deviation coefficient when correlation time is sufficiently large and finally trends toward a constant value which is completely determined by input current. Further, the present results will be benefit to investigate the functional roles of randomness in neural spiking. [ABSTRACT FROM AUTHOR]