A novel strategy for suppressing subsynchronous resonance (SSR) in power systems using a superconducting magnetic energy storage (SMES) unit is presented. The energy transfer between the power system and the SMES unit is based on simultaneous control of active and reactive power modulation of the SMES unit. The active power is controlled by an artificial neural network (ANN) based controller, while the reactive power is controlled by a conventional regulator. The gains of the controllers are determined from the power system operating conditions and the rating of the SMES unit. Unequal alpha-mode of firing angle control of the converters is utilized to enforce zero energy transfer in the SMES unit under steady state conditions. The proposed scheme is tested using the IEEE first benchmark model for subsynchronuos oscillations, and it is found that, with the proposed mode of control, the SMES unit can effectively restore power system stability.