<p>A predefined-time geometric sliding mode control scheme is developed for a free-flying space manipulator on Lie group SE(3) in the presence of model uncertainties and unknown external disturbances. Firstly, considering the singularity and nonuniqueness limitations inherent in attitude parameterization strategies, the kinematics and dynamics of the system are formulated on SE(3). According to proper error configuration functions, the configuration error matrices on SE(3) are converted to configuration error vector and velocity error vector in Euclidean space. Then, to ensure the predefined-time stability for translational and rotational tracking on SE(3), a novel nonsingular terminal sliding mode (NTSM) surface and a geometric NTSM controller are proposed for the error vectors. In addition, a radial basis function neural network and adaptive law are integrated into the designed control scheme, which can accurately estimate the bounded uncertainties and approximation errors. By virtue of the properties of the configuration error function serving as a Lyapunov function, the tracking errors under the proposed control scheme are guaranteed to converge to arbitrarily small neighborhoods of zero within the predefined time. Finally, the numerical simulations are carried out to demonstrate the effectiveness, robustness, and superiority of the proposed control scheme.</p>