To make out the signal processing of neuron and neural system, researchers have worked on it for scores of years. In this paper, the responses of FitzHugh-Nagumo (FN) neuron model, which is stimulated by additive Gaussian white noise and weak sinusoidal signal, is investigated via numerical simulations. The time and frequency domain results show that there is stochastic resonance and a dimensionless frequency sensitive range of 0.2-0.8. Thus the model can help to detect the sinusoidal signal. In addition, the frequency sensitivity coincides with the findings in biology and is beneficial to disclosing the secret in the signal transmission of neuron and neural system.