Abstract-This paper considers a trajectory-based approach to determine control signals superimposed to those of existing controllers so as to enhance the damping of electromechanical oscillations. This approach is framed as a discrete-time, multi-step optimization problem which can be solved by model-based and/or by learning-based methods. This paper proposes to apply a model-free tree-based batch mode Reinforcement Learning (RL) algorithm to perform such a supplementary damping control based only on information collected from observed trajectories of the power system. This RL-based supplementary damping control scheme is first implemented on a single generator and then several possibilities are investigated for extending it to multiple generators. Simulations are carried out on a 16-generators medium size power system model, where also possible benefits of combining this RL-based control with Model Predictive Control (MPC) are assessed.