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Synchronization in a two-small-world-layer neuronal network is studied.For a single-layer network with small-world connection of HR neurons,chaotic burst synchronization and nearly complete synchronization can be observed if the link probability is large enough.For a neuronal network coupled by two single-layer networks with link probability differences between layers,we find that the two-layer network can achieve synchrony as the interlayer coupling strength increases.When chaotic layer network is coupled with chaotic-burst-synchronization layer network,the latter is dominant at small interlayer coupling strength gin,so it can make the layer with the irregular pattern show some regular and also exhibit the same pattern with the other layer.However,when chaotic layer is coupled with nearly-complete-synchronization layer,the ordered layer is dominated by a disordered one with gin increasing.Therefore,the synchronous states strongly depend on the interlayer coupling strength and the link probability.