We study the stochastic resonance (SR) in Hodgkin-Huxley (HH) neural systems with small-world (SW) connections under the noise synaptic current and periodic stimulus, focusing on the dependence of properties of SR on coupling strength c. It is found that there exists a critical coupling strength c* such that if c＜c*, then the SR can appear on the SW neural network. Especially, dependence of the critical coupling strength c* on the number of neurons N shows the monotonic even almost linear increase of c* as N increases and c* on the SW network is smaller than that on the random network. For the effect of the SW network on the phenomenon of SR, we show that decreasing the connection-rewiring probability p of the network topology leads to an enhancement of SR.This indicates that the SR on the SW network is more prominent than that on the random network (p = 1.0).In addition, it is noted that the effect becomes remarkable as coupling strength increases. Moreover, it is found that the SR weakens but resonance range becomes wider with the increase of c on the SW neural network.