This paper presents an adaptive wide-area damping controller (WADC) based on generalized predictive control (GPC) and model identification for damping the inter-area low frequency oscillations in large-scale inter-connected power system. A recursive least-squares algorithm (RLSA) with a varying forgetting factor is applied to identify online the reduced-order linearlized model which contains dominant inter-area low frequency oscillations. Based on this linearlized model, the generalized predictive control scheme considering control output constraints is employed to obtain the optimal control signal in each sampling interval. Case studies are undertaken on a two-area four-machine power system and the New England 10-machine 39-bus power system, respectively. Simulation results show that the proposed adaptive WADC not only can damp the inter-area oscillations effectively under a wide range of operation conditions and different disturbances, but also has better robustness against to the time delay existing in the remote signals. The comparison studies with the conventional lead-lag WADC are also provided.