In this paper, a nearly optimal neuro-controller is developed by using adaptive dynamic programming (ADP) for the single shaft heavy-duty gas turbine (GT). Unlike the conventional controllers, the neuro-controller consists of two neural network (NN) structures: the critic and action network. The critic network learns to approximate the cost-to-go or strategic utility function and uses the output of action network as one of its inputs. The action network outputs the control action to minimize the output of critic network. Moreover, the neuro-controller can be designed by using pre-recorded data from GT system operation, and offline training, thus the computational load of online training and the issues of instability are avoided. Finally, simulation results are presented to show that ADP based neuro-control is much more effective than the conventional PID control for improving dynamic performance and stability of GT system under small and large disturbances.