Through the feedback of the rotor speed and/or the grid frequency, an energy storage system (ESS) can effectively suppress the electromechanical oscillation of a power system. This paper proposes a novel control strategy and controller parameter design method for ESSs to achieve the desired performance of oscillation suppression, including smaller frequency and rate of change of frequency (ROCOF) deviation than their threshold values. Firstly, a dynamic model of the electromechanical time scale of a synchronous generator dominated power system with ESS was established. Then, based on the dynamic model and the electric torque analysis method, the mechanism of an ESS with the feedback signal of the rotor speed to suppress the electromechanical oscillation was investigated. Finally, the controller parameter design method for the ESS was developed to achieve the desired performance of oscillation suppression. With the help of the well-designed ESS, the electromechanical oscillation of a synchronous generator dominated power system can be effectively suppressed in shorter transient response times, and the grid frequency deviation and the ROCOF can be limited to below their threshold values. The simulation results also verify the effectiveness of the proposed control strategy and the controller parameter design method.