A dual adaptation generalized predictive controller (DA-GPC) capable of synchronous modeling and tuning in real time is proposed. The distinctive feature of the proposed controller is the utilization of a second order discrete time controlled auto-regressive integrated moving average (CARIMA) model to capture all possible variations of numerator dynamics via the variable forgetting factor recursive least squares (VFF-RLS) algorithm. The evolving dynamic model is then used to tune, in real time, the value of the move suppression weight. Simulation studies on two benchmark process control problems, i.e., the Van de Vusse nonlinear isothermal stirred tank reactor (with dead time) and the strong acid-base neutralization process, revealed the improved performance of the DA-GPC scheme over the traditional model adaptive GPC and the conventional GPC schemes in terms of set point tracking. Further simulation studies revealed that the DA-GPC scheme was adept in rejecting load disturbances in the process. The good performance attained was attributed to the judicious adaptation of the move suppression weight. Moreover, a user-friendly aspect of the DA-GPC scheme is that the only parameter requiring manual tuning is the VFF-RLS parameter (σ), which may span a large range without materially affecting the efficacy of this adaptive controller.