This article introduces a robust adaptive control development to deal with internal uncertainties and external disturbances on Internet-based robotic teleoperation systems with time-varying delay. Modelling uncertainties are one of the critical challenges in control design procedure for robotic systems. In teleoperation applications interacting with unknown remote environment, latency of communication networks jeopardises stability and performance of the system. Adaptive algorithms are capable of guaranteeing the system's stability and performance under time-varying delay and uncertainties. Hence, based on the maximum magnitude of those disturbances, an adaptive control methodology is applied on an Internet-based teleoperation system to robustify its stability and performance. An extensive simulation study demonstrates effectiveness of the developed control technique.