A neural network-based approximate dynamic programming (ADP) method, the direct neural dynamic programming (direct NDP), is introduced in this paper. The paper covers the basic principle of this learning scheme and an illustrative example of how direct NDP can be implemented. The paper focuses on how direct NDP can be applied to power system stability control. In this case direct NDP is based on real-time system measurements provided by wide area measurement system (WAMS) to compensate for nonlinearities and uncertainties in the system. The learning objective used in controller design makes use of a reward function that reflects system global characteristics if available. This learning control mechanism is adopted in the implementation of a static var compensator (SVC) supplementary damping control and two DC power modulation control systems. The design and evaluation of the learning controller and the system performance are evaluated based on simulations of a standard 2-area system. Results demonstrate the adaptive and learning features of the neural controller which is advantageous over traditional control designs.