It is of great importance to simultaneously stabilize output power and suppress platform motion and fatigue loads in floating offshore wind turbine control systems. In this paper, a novel composite blade pitch control scheme considering actuator fault is proposed based on an augmented linear quadratic regulator (LQR), a fuzzy proportional integral (PI) and an adaptive second-order sliding-mode observer. Collective pitch control was achieved via the fuzzy PI, while individual pitch control was based on the augmented LQR. In the case of actuator fault, an adaptive second-order sliding-mode observer was constructed to effectively eliminate the need for the upper bound of unknown fault derivatives and suppress the chattering effect. This paper conducted co-simulations based on FAST (Fatigue, Aerodynamics, Structures, and Turbulence) and MATLAB/Simulink to verify the effectiveness and superiority of the proposed scheme under different environmental conditions. It is shown that platform roll was reduced by approximately 54% compared to that under PI control. For the tower fore–aft moment, load reductions of 45% or more were achievable. The proposed scheme can greatly reduce the pitch and roll of the floating platform and loads in the windward direction of the wind turbine.