This paper studies the global asymptotic stabilization of a class of upper-triangular systems without a priori knowledge of control directions under the homogeneous domination. The homogeneous domination is used in this paper to design state feedback controllers. The Nussbaum-type gain method is also introduced to complete the design of the controller. The controller is not only used to ensure the global boundedness for all signals of the closed-loop system, but also to guarantee that the system state asymptotically converges to zero. Finally, the simulation results are given to illustrate the effectiveness of the proposed approach.