Neural networks are dynamic systems consisting of highly interconnected and parallel nonlinear processing elements that are shown to be extremely effective in computation. This paper presents an architecture of recurrent neural networks for solving the N-Queens problem. More specifically, a modified Hopfield network is developed and its internal parameters are explicitly computed using the valid-subspace technique. These parameters guarantee the convergence of the network to the equilibrium points, which represent a solution of the considered problem. The network is shown to be completely stable and globally convergent to the solutions of the N-Queens problem. A fuzzy logic controller is also incorporated in the network to minimize convergence time. Simulation results are presented to validate the proposed approach.