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A G m C-style state constrained neuron (SCN) model for the design of processors in analog recurrent neural networks such as Hopfield neural networks, cellular nonlinear networks for combinatorial optimization is described. The unconstrained neurons which have the free state variable, could be stable at any arbitrary point in the solution space or trapped by un-intentional effects. These may introduce errors. For the unconstrained network, the solution could be different from the expected one due to the discrepancy in the energy function of the network and the objective function to be optimized. In addition, if the state variable is limited by some neighboring saturated transistors, un-desirable results may be obtained. GmC-style SCN model can ensure the convergence of the network and avoid discrepancy between the energy function of the network and the objective function. The state resistor is also eliminated in the G m C model so that high cell-density can be achieved. Simulation results show that the proposed model is effective in significantly reducing optimization error.