This study considers the problem of finitetime attitude control for quadrotor unmanned aerial vehicles (UAVs) subject to parametric uncertainties, external disturbances, input saturation, and actuator faults. Under the strong approximation of radial basis function neural networks (RBFNN), an adaptive finitetime NN observer is first presented to obtain the accurate information of unavailable angular velocity. More importantly, an adaptive mechanism to adjust the output gain of the fuzzy logic system (FLS) is developed to avoid the selection of larger control gains, and can even work well without the prior information on the bound of the lumped disturbance. Based on the nonsingular fast terminal sliding mode manifold, a novel switching control law is designed by incorporating the adaptive FLS and fast continuous controller in order to remove the undesired chattering phenomenon and solve the negative effects induced from the parametric uncertainty, external disturbance, and actuator fault. To deal with the input saturation, an auxiliary system is constructed. The rigorous theoretical analysis is given to prove that all the signals in the closed-loop system are uniformly bounded, and tracking errors converge into bounded neighborhoods near the origin in finite time. Moreover, the issue of selecting control parameters is analyzed in detail. Last but not least, the comparative simulation results show the validity and feasibility of the proposed control framework.