The purpose of this paper is to drive the adaptive multi-rate generalized predictive control for multi-variable systems in a stochastic framework. Modelling disturbances as white noise is inadequate for process control because most disturbances encountered in process control are coloured or non-stationary in nature. For that reason a stochastic parallel model identification algorithm for a multi-rate-sampled system is proposed. No attempt is made to identify the noise model. Hence the algorithm is applicable to any measurement noise case. The measurement noise can be arbitrary (for example coloured or non-stationary noise), except for the assumption that it and control inputs are stochastically uncorrelated. Then the control algorithm based on the generalized predictive control is proposed. In order to demonstrate the effectiveness of the proposed control algorithm a simulation study is carried out. The closed-loop performances are excellent.