Robot manipulators, which are nonlinear structures and have uncertain system parameters, are complex dynamically when operated in an unknown environment. To compensate for estimate errors of the uncertain system parameters and to accomplish the desired trajectory tracking, nonlinear robust controllers are appropriate. However, when estimation errors or tracking errors are large, they require large input torques, which may not be satisfied due to torque limits of actuators such as driving motors. As a result, their stability cannot be guaranteed. In this paper, a new robust control scheme is presented to solve stability problems and to achieve fast trajectory tracking of uncertain robot manipulators in the presence of torque limits. By using fuzzy logic, new desired trajectories which can be reduced are generated based on the initial desired trajectory, and torques of the robust controller are regulated so as to not exceed torque limits. Numerical examples are shown to validate the proposed controller using an uncertain two degree-of-freedom underwater robot manipulator.