An adaptive first-order W-E generalized analytical predictor (GAP) is presented lo overcome the difficulty that is caused by possible changes in the load transfer function for output disturbances. An on-line adaptive algorithm for updating the parameter in the load transfer function is derived and the convergence of the algorithm is also analysed. This algorithm contains tuning parameters that can be chosen for the purpose of its robust stability. The proposed adaptive W-E GAP is implemented during the second phase of a two-phase adaptive system for predictive control.