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State estimation for uncertain systems affected by external noises has been recognized as an important problem in control theory for either discrete and continuous plants. This paper deals with the state observation problem when the discrete-time dynamic model of a plant is partially unknown and it is affected by some sort of uncertainties and external perturbations. Recurrent Neural Networks (RNN) have shown several advantages to treat many different control and state estimation problems. In this paper, a new discrete-time Luenberger-like observer using the structure of a RNN is proposed. The class of discrete-time nonlinear system just has the input-output pairs as available information. The neural observer is training off-line using a class of least mean square method for matrix parameters. Lyapunov theory is employed to obtain the upper bounds for the weights dynamics as well for the estimation error and the learning laws to ensure the convergence of the observer. Simulation results using the van der Pol oscillator as data generator are presented to demonstrate the effectiveness of the proposed neural observer.