In this paper, a model reference controller (MRC) based on a neural network (NN) is proposed for damping oscillations in electric power systems. Variation in reactive load, internal or external perturbation/faults, and asynchronization of the connected machine cause oscillations in power systems. If the oscillation is not damped properly, it will lead to a complete collapse of the power system. An MRC base unified power flow controller (UPFC) is proposed to mitigate the oscillations in 2-area, 4-machine interconnected power systems. The MRC controller is using the NN for training, as well as for plant identification. The proposed NN-based MRC controller is capable of damping power oscillations; hence, the system acquires a stable condition. The response of the proposed MRC is compared with the traditionally used proportional integral (PI) controller to validate its performance. The key performance indicator integral square error (ISE) and integral absolute error (IAE) of both controllers is calculated for single phase, two phase, and three phase faults. MATLAB/Simulink is used to implement and simulate the 2-area, 4-machine power system.