This paper investigates a novel offset-free control scheme based on a multiple model predictive controller (MMPC) and an adaptive integral action controller for nonlinear processes. Firstly, the multiple model description captures the essence of the nonlinear process, while keeping the MPC optimization linear. Multiple models also enable the controller to deal with the uncertainty associated with changing setpoint. Then, a min-max approach is utilized to counter the effect of parametric uncertainty between the linear models and the nonlinear process. Finally, to deal with other uncertainties, such as input and output disturbances, an adaptive integral action controller is run in parallel to the MMPC. Thus creating a novel offset-free approach for nonlinear systems that is more easily tuned than observer-based MPC. Simulation results for a pH-controller, which acts as an example of a nonlinear process, are presented to demonstrate the usefulness of the technique compared to using an observer-based MPC.