On the basis of the theoretical analysis of a single-machine infinite-bus (SMIB), using the modified linearized Phillips-Heffron model installed with unified power flow controller (UPFC), the potential of the UPFC supplementary controller to enhance the dynamic stability of a power system is evaluated by measuring the electromechanical controllability through singular value decomposition (SVD) analysis. This controller is tuned to simultaneously shift the undamped electromechanical modes to a prescribed zone in the s-plane. The problem of robust UPFC based damping controller is formulated as an optimization problem according to the eigenvalue-based multi-objective function comprising the damping factor, and the damping ratio of the undamped electromechanical modes to be solved using gravitational search algorithm (GSA) that has a strong ability to find the most optimistic results. The different loading conditions are simulated on a SMIB system and the rotor speed deviation, internal voltage deviation, DC voltage deviation and electrical power deviation responses are studied with the effect of this flexible AC transmission systems (FACTS) controller. The results reveal that the tuned GSA based UPFC controller using the proposed multi-objective function has an excellent capability in damping power system with low frequency oscillations and greatly enhances the dynamic stability of the power systems.