In this paper, we study the output feedback tracking problem of position tracking for a class of single-link robot system with completely unknown parameters under the assumption that time varying reference signal and its first derivative have unknown upper bounds. To handle this problem, we construct a novel adaptive tracking controller with appropriate design parameters combining the methods of universal control and dead zone with backstepping technique. The constructed controller can guarantee the state of the resulting closed-loop system is globally bounded, and the tracking error belongs to an arbitrarily small interval of the origin after a finite time. Finally, the results of the simulation illustrate that the proposed method is effective.