The sub-& super-synchronous control interaction (SSCI) between direct-driven wind turbine generators in offshore windfarm and AC power grid probably cause an unusual stability problem, which seriously restricts the consumption and utilization of offshore wind power. The chracteristics of SSCI are varying with the operating conditions and the number of wind turbine generators, which have brought a great challenge for the design of SSCI suppression method. In this paper, a grid-side supplementary damping control (SDC) scheme based on static var generator (SVG) is proposed to stabilize SSCI in offshore wind farms. Firstly, the impedance-based analysis reveals the mechanism for SDC to suppress the SSCI. Then, the structure of SDC and the parameter optimization method based on damping maximization are introduced. Finally, the oscillation suppression effect of SDC is verified by electromagnetic transient simulation, which shows that the proposed SDC can provide positive damping in a wide range of oscillation frequencies, and the performance demonstrates that SDC can improve the impedance characteristics of the wind farm in the sub-& super-synchronous frequency, and effectively suppress the SSCI caused by offshore direct drive wind turbines.