This paper investigates the finite-time position trajectory tracking control problem of quadrotor unmanned aerial vehicles (UAVs). Different from the standard inner-outer-loop control scheme, the proposed finite-time controller is constructed with an order-supplementary mechanism. Concretely, some virtual extended states with second-order dynamics are utilized in the controller design of the quadrotor's position-loop subsystem, to replace the original state error feedback part. Then, the adding a power integrator technique is used in the establishment of the virtual state dynamics, such that the position closed-loop subsystem achieves the trajectory tracking in finite time. Meanwhile, the attitude command references are directly formulated from the virtual extended states. Moreover, to deal with the problems of quadrotor disturbances or unknown velocities, some finite-time observers are combined in the proposed approach to obtain and compensate/replace the disturbances/unknown velocities. Compared with the existing results, the proposed order-supplementary finite-time trajectory tracking approach can remove the use of the filters in the attitude command resolution and realize the strict finite-time convergence. Thrust control inputs for the position-loop subsystem can be adjusted more flexibly by setting the initial values of the virtual states. In addition, the finite-time velocity observer provided in this paper takes aerodynamic damping into account and has more accurate observations in practice. Some simulations are given to validate the effects of the proposed approach.