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This paper proposes a new approach for constrained multivariable predictive control based on the use of a recurrent neural network as a non-linear prediction model of the plant under control. The model is derived in a natural way from its linear counterpart, and it is a representation of the system in the state-space form. The proposed predictive control scheme is able to deal with constraints in the system variables and highly non-linear dynamics. As an example model, a sulphitation tank taken from the sugar industry has been modelled and controlled with the proposed neural predictive controller. Comparisons with a PI and a generalized predictive controller are also given, showing the reliability of the proposed neural predictive control.