In this paper a new model predictive control (MPC) strategy, applicable to a set of nonlinear systems, is proposed and the use of it is demonstrated on a model of a waste treatment reactor. The MPC strategy is an extension of earlier work in optimization-based control . The motivation for the study is to search for approaches to nonlinear MPC without having to solve the full nonlinear problem. We restrict our problem by defining a nonlinear model set as a convex combination of a set of bounding linear models. The weighting factors between the models can be a function of the states and/or inputs. At a given time-instant we compute an optimal future control sequence for each of the bounding linear models. A novel feature is that all models must obey the constraints for each of the control sequences. The reason for these additional constraints is that they provide us with feasibility guarantees. It also is a means of robustifying the MPC. The final control sequence is found by interpolating the control sequences derived from the optimization problems. There are different possible approaches for choosing the interpolation variables. Provided the optimization criterion and the constraint sets for the control variables and states are convex, the proposed control algorithm involves only convex optimization problems. The interpolating MPC strategy is applied to a waste treatment reactor, where the process dynamics are nonlinear and time-varying depending on the disturbance. Linearization is carried out to obtain bounding models for the process. The interpolating MPC is designed based on the bounding models. Through the example we demonstrate significant improvements over a standard quadratic MPC strategy based on linear models.