A self-organized network model based on two-dimensional cellular automaton was presented. We studied the critical characteristic and long-range dependence in the networks. Every cell in the model comprises one router and random number of hosts, and it can regulate the rate of packet release of the hosts according to the congestion state perceived by the cell. It is shown that under the control of the congestion-control-mechanism, the network is poised at critical state, although heterogeneity exists obviously in the nodes, the queue length of the nodes also exhibits strong spatial and temporal correlation.