Robot teleoperation techniques are applied in industrial automation, space, and surgery. Considering the high cost of force–torque (F/T) sensors, an “indirect estimation” of the external force is preferable to “direct sensing” of the force. This study provides a predictive control method for a bimanual teleoperation system without F/T and acceleration sensors. Two types of mirror predictors are built into the control architecture. One of them is a position predictor estimating the position states of the remote side under stochastic network-induced delays. The force predictor estimates the contact forces and dynamic uncertainties utilizing the local time-delayed information. By accurately estimating the local force, the position predictors/observers are used to estimate the internal dynamics of the master and slave simultaneously, and thereby, avoid using the delayed transmitted information. An adaptive fuzzy control strategy based on linear matrix inequalities (LMIs) is proposed to evaluate and suppress the uncertainties, thereby, ensuring that the synchronization errors of the system positions converge to zero and the estimated force approaches real values. The system stability of the closed-loop system is proven using LMIs based on a Lyapunov–Krasovskii functional synthesis. An experimental test involving a dual-arm robot, YuMi, holding and moving a yoga ball is performed based on a semiphysical platform.