We study the effects of the strength of coupling between neurons on the spiking regularity and coherence in a complex network with randomly connected Hodgkin-Huxley neurons driven by colored noise. It is found that for the given topology realization and colored noise correlation time, there exists an optimal strength of coupling, at which the spiking regularity of the network reaches the best level. Moreover, when the temporal regularity reaches the best level, the spatial coherence of the system has already increased to a relatively high level. In addition, for the given number of neurons and noise correlation time, the values of average regularity and spatial coherence at the optimal strength of coupling are nearly independent of the topology realization. Furthermore, there exists an optimal value of colored noise correlation time at which the spiking regularity can reach its best level. These results may be helpful for understanding of the real neuron world.