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This paper investigates the effect of superconducting magnetic energy storage (SMES) unit in stabilising multi-mode torsional oscillations of sub-synchronous resonance (SSR) of a large turbine-generator set. The study is performed on system-1 of the second IEEE benchmark model for computer simulation of subsynchronous resonance. Modal control theory is used to determine the parameters of the SMES control loops. To prove the effectiveness of the proposed controller, eigenvalues of the system with and without the SMES unit are given. Dynamic simulations are performed using the nonlinear system model. Results show that the proposed controller is very effective in damping all SSR modes of the system under study. The proposed controller is simple and easy to be implemented.