The position control of robot manipulators has been recognized as the most fundamental and simplest objective in the robotic control field. For the high-precision position control problem of the multi-axis robot system, this study proposed a simple output feedback nonlinear PD plus gravity compensation (PD+ ) synchronization position controller combining with the cross-coupling techniques. The global finite-time stability of closed-loop systems was strictly demonstrated by applying Lyapunov stability theory and geometric homogeneity techniques. Compared with the asymptotic stable full-states feedback control schemes, the presented controller ensures the finite-time stability of the robot manipulators with position measurements only; compared with the output feedback asymptotic stable controllers, the proposed controller ensures the finite-time convergence of robot’s states; compared with the output feedback controllers without synchronization term, the proper introduction of nonlinear synchronization control items enables the proposed controller to take into account the synchronous and coordinated motion between the axes on the premise of ensuring the high-precision position control of the multi-axis robot system. The proposed controller has the advantages of simple structure, easy implementation, faster response speed and better overall system performance, which meets the high precision requirements of actual production for the robot system. Numerical simulation results demonstrate the effectiveness of the proposed control algorithm and the expected performance of the system. The proposed control method not only ensures the global output feedback finite-time stable synchronization control of multi-axes robot systems, but also provides an effective alternative approach for the output feedback synchronization position stabilization of a large class of nonlinear second-order systems.