In this paper, a goal representation heuristic dynamic programming (GrHDP) based controller is developed for the doubly-fed induction generator based wind farm to improve the system transient stability under fault conditions. The proposed controller is based on adaptive dynamic programming (ADP) techniques to approximate the optimal control policy according to the interaction between the controller and the power plant. Compared to existing ADP approaches with one action network and one critic network, our GrHDP architecture introduces an additional network, i.e., the reference network, to form an internal goal/reward representation. This better mapping between the system state and the control action significantly improves the control performance. The effectiveness of the proposed approach is validated via two cases. The first case investigates a revised four-machine two-area system with high wind penetration and a static synchronous compensator. The second case is a practical size power system with wind farm in Liaoning Province in China. Detailed simulation analysis and comparative studies with traditional ADP approaches are presented to demonstrate the superior performance of our method