Flywheel energy storage system（FESS） can be used for damping power system low-frequency oscillations by compensating for the imbalance power with appropriate control strategy， which has an independent active and reactive power control capability. The principle of damping power system low-frequency oscillations with FESS is theoretically investigated by damping torque analysis（DTA） method. A method is also proposed to select the best installing location， damping control loop， feedback signal based on DTA and to design FESS-based stabilizer by the phase compensation method. All of the analytical conclusions have been confirmed by the results of eigenvalue calculation and non-linear simulation by a four-machine power system example.