This paper focuses on the problem of predefined-time adaptive output-feedback tracking control with prescribed performance for a quadrotor unmanned aerial vehicle (QUAV). By applying the command filter, the “explosion of complexity” problem is effectively avoided, and the effect of filtered error is removed by virtue of the fractional power error compensation mechanism simultaneously. A fuzzy state observer is devised to estimate the unmeasurable states of QUAV. The singularity problem is successfully surmounted by the property of hyperbolic tangent functions. The predefined-time performance function is introduced to ensure the tracking errors are restrained to the prescribed performance bounds. It is strictly proved that the closed-loop system is practically predefined-time stable, and tracking errors converge to a small region around zero within a predefined time. Finally, a simulation example shows the effectiveness of the proposed predefined-time tracking control scheme.