Aiming at the uncertainty problems of unknown speed measurement and multi-source disturbances in the trajectory tracking process of a quadrotor UAV, a composite non-singular fast terminal sliding mode control scheme based on an adaptive reduced-order generalized parameter estimation-based observer (GPEBO) is proposed. Firstly, considering the position and attitude loop characteristics of the system, a linear regression equation is constructed after the system is re-parameterized to transform the state estimation of the system into parameter estimation. Next, the adaptive reduced-order GPEBO with finite-time convergence is designed by introducing dynamic regression extension and mixing theory to reconstruct the unknown speed measurement value and estimate the lumped interference. Then, a dynamic non-singular fast terminal sliding surface is constructed based on the reconstructed state, and a composite non-singular fast terminal sliding mode controller with finite-time convergence is designed in the position and attitude loops based on the estimated lumped interference information combined with a non-singular fast terminal sliding mode controller. The Lyapunov method proves the finite-time convergence proof of the closed-loop system. Finally, the simulation results show that the proposed method has a faster convergence speed and better anti-disturbance ability than the composite control based on an extended state observer.