In this paper, a novel method is constructed for model predictive control (MPC) of multi-input multi-output (MIMO) systems. The latter are represented by a discrete-time MIMO ARX model expansion on Laguerre orthonormal bases. The resulting model, entitled the MIMO ARX-Laguerre model, provides a recursive representation with parameter number reduction. This reduction is strongly linked to the choice of Laguerre poles, and therefore we propose a new algorithm to optimize the Laguerre poles of the resulting model. The recursive formulation of the MIMO ARX-Laguerre model is used to obtain the MPC strategy. An 2-norm finite moving horizon cost function is used to obtain a control law which is implemented as a quadratic programming (QP) problem. The effectiveness of the proposed controller that takes into account physical constraints is illustrated by a numerical simulation example and by a practical validation on an experimental communicating two-tank system (CTTS).