The aerial manipulator is a crucial equipment for dismantling and installing current-carrying clip bolts during substation maintenance operations. To address the issues of slow error convergence and performance degradation caused by unknown disturbances during the visual servoing tracking of the bolts, this paper proposes a non-singular terminal integral sliding mode control method based on an integral sliding mode disturbance observer. The proposed method establishes the kinematic model of the image-based visual servoing system and analyzes the effect of external disturbances on model uncertainty, which is further characterized using an equivalent disturbance term. A non-singular terminal integral sliding mode controller incorporating an integral power term and a non-singular terminal term is designed. Combining with an exponential reaching law, the non-singular terminal integral sliding mode control law is derived, guaranteeing the rapid convergence of the system tracking error in finite time. Furthermore, an integral sliding mode variable is used to construct a dynamic observation equation, from which the system state and disturbance estimation equations of the integral sliding mode disturbance observer are derived. The estimated disturbance values are then feedforward compensated into the sliding mode control law, enhancing the system′s disturbance rejection performance. The stability of the system and the finite-time convergence of the tracking error are proven using Lyapunov theory. Finally, simulation experiments verify the feasibility of the proposed method. Additionally, an aerial operation simulation platform is constructed to design dynamic target tracking experiments under various disturbance conditions. The experimental results show that the proposed method reduces the average convergence time by 4.92 s and decreases the root mean square error by an average of 11.03 pixels compared to the benchmark methods. It consistently improves convergence speed and tracking accuracy under various unknown disturbance conditions. Furthermore, the designed sliding surface exhibits favorable dynamic performance, and the disturbance observer accurately estimates external disturbances, indicating strong potential for practical engineering applications.