To address the impact of modeling errors and unknown external disturbances on the trajectory tracking accuracy of robotic arm systems in practical applications, an adaptive non-singular fast terminal sliding mode control strategy based on a nonlinear disturbance observer (ANFTSMC-DO) is designed. First, a nonlinear disturbance observer is devised to estimate disturbance information online. By selecting an appropriate nonlinear gain function, the estimation error converges rapidly in an exponential manner. Next, an adaptive non-singular fast terminal sliding mode controller is employed to handle parameter variations and unmodeled dynamics, preventing system performance degradation over time. Meanwhile, under the premise of ensuring robust stability and control accuracy, the proposed method effectively suppresses chattering, thereby enhancing resistance to external disturbances. Finally, simulations verify the effectiveness of the proposed method.