The paper presents a digital adaptive controller of recurrent neural networks for the active flutter suppression of a wing structure over a wide transonic range. The basic idea behind the controller is as follows. At first, the parameters of recurrent neural networks, such as the number of neurons and the learning rate, are initially determined so as to suppress the flutter under a specific flight condition in the transonic regime. Then, the controller automatically adjusts itself for a new flight condition by updating the synaptic weights of networks online via the real-time recurrent learning algorithm. Hence, the controller is able to suppress the aeroelastic instability of the wing structure over a range of flight conditions in the transonic regime. To demonstrate the effectiveness and robustness of the controller, the aeroservoelastic model of a typical fighter wing with a tip missile was established and a single-input/single-output controller was synthesized. Numerical simulations of the open/closed-loop aeroservoelastic simulations were made to demonstrate the efficacy of the adaptive controller with respect to the change of flight parameters in the transonic regime.