This paper presents an approach for the constrained non-linear predictive control problem based on the input-output feedback linearization (IOFL) of a general non-linear system modelled by a discrete-time affine neural network model. Using the resulting linear system in the formulation of the original non-linear predictive control problem enables to restate the optimization problem as the minimization of a quadratic function, which solution can be found using reliable and fast quadratic programming (QP) routines. However, the presence of a non-linear feedback linearizing controller maps the original linear input constraints onto non-linear and state dependent constraints on the controller output, which invalidates a direct application of QP routines. In order to cope with this problem and still be able to use QP routines, an approximate method is proposed which simultaneously guarantees a feasible solution without constraints violation over the complete prediction horizon within a finite number of steps, while allowing only for a small performance degradation.