To anti-vibration control of floating wind turbines, the underactuated translational Oscillator with Rotating Actuator (TORA) consisting of one unactuated translational cart and one actuated rotor is adapted in the nacelle of floating wind turbine acting as a damper. We analyze the effect of new proposed disturbance observer-based sliding mode control (SMC) law on nonlinear TORA system suffering vibration of the floating wind turbine as unknown exogenous disturbance. For this we design a new sliding mode surface, which is a combination of traditional, integral and terminal sliding mode surfaces along with the output of disturbance observer for canceling the effect of above-mentioned disturbance. A complete theoretical proof with simulation result is described here, for the feasibility of this new disturbance observer-based SMC.