In this paper, the position tracking control with finite-time convergence has been studied for a class of nonliear uncertain robot manipulators. Radial basis function neural network (RBFNN) based adaptive control is designed to compensate for the effect of the unknown dynamics. To achieve the finite-time convergence of both trajectory tracking error and RBFNN learning error, barrier Lyapunov functions (BLFs) and and filtering techniques are employed to design a performance function and a tracking error region to ensure position tracking error converge to a pair of specified bounds in a finite time. The effectiveness and efficiency of the proposed control method is tested and verified by simulation studies.