The design of a Model Predictive Control (MPC) algorithm for quasi Linear Parameter Varying (qLPV) systems is developed herein. An online Least-Squares procedure that computes the future evolution of the qLPV scheduling parameters is at the core of the proposed method, which enables the replacement of a complex nonlinear optimization by a (much simpler) Quadratic Programming Problem (QP) one. The method also uses contractive terminal set constraints and a Lyapunov-associated terminal cost to the MPC QP, so that the domain of attraction of this controller is enlarged and feasibility is guaranteed. This paper ends with a successful simulation of this technique applied to the control of vehicular suspensions.