This article focuses on global finite-time output feedback stabilization for uncertain nonlinear systems with unknown measurement sensitivity. The existence of the continuous measurement error resulting from limited accuracy of sensors invalidates the existing design strategies depending on the use of the precise output in the construction of an observer, which highlights the contribution of this article. Essentially, different from related works, we propose a new finite-time convergent observer by avoiding the use of the information on nonlinearities. By combining the homogeneous domination with the addition of a power integrator method, an output feedback controller composed of multiple nested sign functions is successfully developed. Finally, the effectiveness of the presented scheme is exhibited by a numerical example.