A Lyapunov-based recurrent neural networks unified power flow controller (UPFC) is developed for improving transient stability of power systems. First, a simple UPFC dynamical model, composed of a controllable shunt susceptance on the shunt side and an ideal complex transformer on the series side, is utilized to analyze UPFC dynamical characteristics. Secondly, we study the control configuration of the UPFC with two major blocks: the primary control, and the supplementary control. The primary control is implemented by standard PI techniques when the power system is operated in a normal condition. The supplementary control will be effective only when the power system is subjected by large disturbances. We propose a new Lyapunov-based UPFC controller of the classical single-machine-infinite-bus system for damping enhancement. In order to consider more complicated detailed generator models, we also propose a Lyapunov-based adaptive recurrent neural network controller to deal with such model uncertainties. This controller can be treated as neural network approximations of Lyapunov control actions. In addition, this controller also provides online learning ability to adjust the corresponding weights with the back propagation algorithm built in the hidden layer. The proposed control scheme has been tested on two simple power systems. Simulation results demonstrate that the proposed control strategy is very effective for suppressing power swing even under severe system conditions.