In this paper stochastic resonance of FHN neuron model when there exists only the response of suprathreshold oscillation with weak periodic signal is studied. The results of research show: A bifurcation of transition from two attractors (suprathreshold oscillation and sub-threshold oscillation) to one attractor (suprathreshold oscillation) occurs with the increase of bifurcation parameter, when the bifurcation parameter of system is on the right side of bifurcation point there exists only the response of suprathreshold oscillation in FHN neuron model excited by weak signal, in this case, under the modulation of external noise or internal noise, the energy of system response concentrating on the frequency of input signal, and the curve of signal - noise - ratio (SNR) of system response vs noise extensity is a mon - peak curve, stochastic resonance occurs, and the mechanism of stochastic resonance in this case is related to the transitions among the three attractors ( two before bifurcation and one after it) on the left and right sides of bifurcation point.