In recent times, renewable energy demand is rapidly increasing worldwide. Offshore wind energy is one of the alternative solutions to the problems posed by non-renewable energy resources. The kinetic energy of the wind is converted to mechanical energy by using an offshore floating wind turbine (OFWT). The efficiency of the OFWT is dependent upon the vibrational effect induced by the environment. In this paper, for the mitigation of this vibrational effect, a new model of barge-type OFWT is designed by using an active control strategy called translational oscillator with a rotational actuator (TORA). The disturbance observer (DO) based advanced control techniques including robust backstepping sliding mode control (BSMC), backstepping integral sliding mode control (BISMC), backstepping nonsingular terminal sliding mode control (BNTSMC), and a new backstepping integral nonsingular terminal sliding mode control (BINTSMC) technique, are devised for the stabilization of OFWT model. The comparison of these techniques is carried out by using MATLAB/SIMULINK which validates the feasibility and correctness of the proposed OFWT model and control techniques.