A receding-horizon (RH) optimal control scheme for a discrete-time nonlinear dynamic system is presented. A non-quadratic cost function is considered and constraints are imposed on both the state and control vectors. A stabilizing regulator is derived by adding a proper terminal penalty function to the process cost. The control vector is generated by means of a feedback control law computed off-line instead of computing it on-line, as is done for existing RH regulators. The off-line computation is performed by approximating the RH regulator by a multilayer feedforward neural network. Bounds to this approximation are established. Algorithms are presented to determine some essential parameters for the design of the neural regulator, i.e. the parameters characterizing the terminal cost function and the number of neural units in the network implementing the regulator. Simulation results show the effectiveness of the proposed approach.