The continuous finite-time high-precision anti-disturbance control problem for robotic manipulators (RM) under external disturbances and parameter uncertainties is investigated in this article. Firstly, a continuous terminal sliding mode control (CTSMC) is introduced to stabilize the nominal dynamics of the RM in finite time. Secondly, a sliding mode differentiator is employed to estimate the lumped disturbances to its nominal dynamics in finite time. By feedforward compensating the estimation of the lumped disturbances, a continuous composite controller is thus obtained for the RM system. The composite controller enjoys the following superior properties: 1) it is continuous and thus no chattering phenomenon appears; 2) the finite-time convergence property of the RM system under the proposed controller is guaranteed even in the presence of disturbances and uncertainties; 3) the nominal control performance of the proposed method is recovered to the baseline CTSMC method in the absence of disturbances and uncertainties. The excellent properties of the proposed algorithm is demonstrated by simulation studies.