This paper aims to address the open problem of designing a globally stable vision-based controller for robot manipulators. Accordingly, based on a hybrid mechanism, this paper proposes a novel task-space control law attained by taking the gradient of a potential function in SE(3). The key idea is to employ the Visual Simultaneous Localization and Mapping (VSLAM) algorithm to estimate a robot pose. The estimated robot pose is then used in the proposed hybrid controller as feedback information. Invoking Barbalats lemma and Lyapunov's stability theorem, it is guaranteed that the resulting closed-loop system is globally asymptotically stable, which is the main accomplishment of the proposed structure. Simulation studies are conducted on a six degrees of freedom (6-DOF) robot manipulator to demonstrate the effectiveness and validate the performance of the proposed VSLAM-based control scheme.