Stochastic resonance is a common natural phenomenon in nonlinear systems. By studying the relations between the out put signal-to-noise ratio (SNR) of the biologic neural network with small-world character and the rewiring probability p which reflects the effect of small-world,the coupling strength c, amplitude A of input signal, we revealed some regularities of the second super-harmonic stochastic resonance in the biologic neural network, and found that the out put SNR doesn't monotonicly increase as the forcing amplitude A increases, but there exists an optimal value AO for the Hodgkin-Huxley (HH) neural network with small-world character. The out put SNR reaches its maximum when A is equal to AO.