This paper presents a novel Proportional Damping Injection (P + d) control scheme that incorporates a damping regulation strategy and an adaptive method for networked telerobotic systems. Unlike the traditional P + d controller with a fixed damping coefficient, the proposed approach includes a dynamic damping adjuster, designed based on position error, to enhance the position tracking speed and improve the system robustness. To address uncertainties in dynamic models and external forces, Radial Basis Function (RBF) neural networks and an adaptive strategy are employed for dynamic estimation. The closed-loop stability of the teleoperation system was rigorously established using the Lyapunov–Krasovskii method, and the relationship between the controller gains and communication delay boundaries was explicitly derived. Finally, simulations and experimental results validated the system’s stability and effectiveness, demonstrating the advantages of the proposed controller.