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It is widely believed that the brains of human beings work at or near the state of self-organized criticality (SOC). In the present work, we investigate two-dimensional small-world neural networks (2D SWNN) with Bak–Sneppen (BS)-type neurons as their nodes. By taking threshold firing and refractory period as the key features of neurons in the simulations, a few power laws are obtained for suitable range of parameters. The SOC characterized by the power-law distribution of avalanche sizes as well as 1∕ f noise emerges in the present model. Moreover, a set of scaling relations are found to exhibit criticality. The exponent for the power spectrum of all return time is α= 0. 71, which is comparable with what were found in medical experiments.