In this paper, we present a Bayesian prediction approach to improve stability of teleoperation systems over the Internet. Motion and force data flows in a teleoperation system are formulated in discrete time state-space models predicted by Bayesian filters, including the Kalman filter and particle filter. The particle filter, which is known as a robust tracking method in nonlinear and non-Gaussian environments, is used to compensate for the time-varying Internet delay. A stochastic analysis is presented to show stability improvement of a teleoperation system in the case when convergence of a Bayesian predictor is achieved and a generalized form of scattering transformation is used as a control scheme. Experiments are performed using a teleoperation system based on virtual reality. A haptic device is used as a human operator in conjunction with a mechanic-based virtual teleoperator by implementing the proposed Bayesian prediction method. Experimental results show that the proposed method improve stability of an overall teleoperation system in the presence of time-varying delay.