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A nonlinear model predictive control (NMPC) algorithm based on a neural network model is proposed for multivariable nonlinear systems. A multi-input multi-output model is developed using multilayer perceptron (MLP) neural network which is trained by Levenberg-Marquardt algorithm and amplitude modulated pseudo random binary (APRBS) signals with noise as data sets. Model predictive control also uses Levenberg-Marquardt algorithm for the control signal optimization. The control performance is improved by using a disturbance model that compensates both model mismatch and external disturbance. The learning rate of disturbance estimation network changes adaptively to treat the model mismatch differently from the external disturbance. Simulation results using the quadruple-tank are employed to show the effectiveness of the method.