This paper presents a new control strategy for an underactuated horizontal two-link flexible manipulator (HTFM) to realize the global stabilization. First, a homeomorphous coordinate transformation is introduced to the original manipulator system to create a new simple nonlinear system. Then, the new system is divided into the linear and nonlinear parts, and the idea of equivalent-input-disturbance (EID) is used to design a controller that globally and asymptotically stabilizes the new system as goal. The global stabilization control problem for the underactuated HTFM is soloved by the fact that the transformation is homeomorphous. The presented control method just adopts the position information of HTFM to design the stabilizing controller, which can not only reduce the cost of the control system, but also avoid the influence of velocity noises on the control performance effectively. The simulation results show that the stabilizing motion process, stabilizing time and other performances of the underactuated HTFM can achieve satisfactory results.