In this paper, robust adaptive control is designed for pitch and torque control of the wind turbines operating under turbulent wind conditions. The dynamics of the wind turbine are formulated by considering the five degrees of freedom system (rotor angle, gearbox angle, generator angle, flap-wise deflection of the rotor blade, and axial displacement of the nacelle). The controller is designed to maintain the rotor speed, maximize the aerodynamic efficiency of the wind turbine, and reduce the loads due to high wind speeds. Gaussian probability distribution function is used for approximating the wind speed, which is given as the disturbance input to the plant. The adaptive control algorithm is implemented to 2 MW and 5 MW wind turbines to test the robustness of the controller for varying parameters. The simulation is carried out using MATLAB/Simulink for three cases, namely pitch control, torque control, and the combined case. A case study is done to validate the proposed adaptive control using real wind speed data. In all the cases, the results indicate that the rotor speed follows the reference speed and show that the designed controller gives a satisfactory performance under varying operating conditions and parameter variations.