The paper proposes a new robust adaptive control method for a two-link robot manipulator to enhance high tracking control performance despite the presence of dynamic uncertainties and unknown disturbances. The paper examines a Non-Singular Fast Time Sliding Mode (NFTSM) controller based on Wavelet Neural Network (WNN). The Wavelet Network is employed to approximate the upper bound of uncertainties and disturbances. In addition, a compensation term is added to the NFTSM control to attenuate the effect of uncertainties, including unavoidable approximation errors and unknown disturbances. Therefore, to ensure high tracking accuracy, chattering phenomenon reduction, and fast response against approximation errors and uncertainties. The parameters of the controller are tuned online by an adaptive learning algorithm, and online adaptive control laws are determined by the Lyapunov stability theorem. Due to these techniques, the suggested control drives the system to the desired performance where tracking errors converge to zero within a finite time. Simulations performed on a two-link robotic arm demonstrate a higher performance of the proposed adaptive robust NFTSMC based on WNN methodology compared to some advanced control strategies.