This paper deals with distributed adaptive generalized predictive control of a grinding circuit. This multivariable system is commonly used in mineral industries for size reduction. It is characterized by time varying dynamics owing to changes in ore properties and operating conditions. The fresh ore feed rate, the water addition rate, the circulating load and the product fineness are respectively selected as control and controlled variables. The parameters of two single input-single output discrete models are identified using a least-squares algorithm, taking into account the requirements for long-term adaptive control. Numerical results have been carried out using a simulator based on phenomenological models derived from mass balance considerations. The adaptive controller is compared to a fixed parameter controller. These results illustrate the self-tuning ability and the continuous adaptivity of the control strategy. They also highlight that adaptive control is particulary suitable for distributed control.