The actuator fault-tolerant control problem for a variable-pitch quadrotor is addressed under uncertain conditions. Following a model-based approach, the plant nonlinear dynamics are faced with a disturbance observer-based control and a sequential quadratic programming control allocation, where only kinematic data of the onboard inertial measurement unit are required for the fault-tolerant control, i.e., it does not require the measurement of the motor speed nor the current drawn by the actuators. In the case of almost horizontal wind, a single observer handles both faults and the external disturbance. The estimation of the wind is fed forward by the controller, while the actuator fault estimation is exploited in the control allocation layer, which copes with the variable-pitch nonlinear dynamics, thrust saturation, and rate limits. Numerical simulations in the presence of measurement noise show the capability of the scheme to handle multiple actuator faults in a windy environment.