This paper proposes a robust adaptive algorithm that effectively copes with time-varying delay and uncertainties in Internet-based teleoperation systems. Time-delay induced by the communication network, as a major problem in teleoperation systems, along with uncertainties in modeling of robotic manipulators and remote environment warn the stability and performance of the system. A robust adaptive control algorithm is developed to deal with the system uncertainties and to provide a smooth estimation of delayed reference signals. The proposed control algorithm generates chattering-free torques which is one of the practical considerations for robotic applications. In addition, the achieved input-to-state stability gains do not necessarily require high gain control torques to retain the system's stability. Experimental simulation studies validate the effectiveness of the proposed control strategy on a teleoperation system consisting of a Phantom Omni Haptic device and SimMechanics model of the industrial manipulator UR10. The validation of the proposed control methodology was executed through a real-time Internet-based communication established over 4G mobile networks between Australia and Scotland.