Bilateral control is one of the control methods of teleoperation system. The presence of network delays between master and slave robots make the design of bilateral control system challengeable. Because, it seriously deteriorates the performance and possibly makes the system unstable. To overcome the destabilization from network delay, the authors' previous research proposed the model-free time delay compensator. The proposed compensator does not utilized time delay model and plant model, but the bilateral control system is stabilized. In this paper, the bilateral control system with dual model-free compensator has been proposed. The model-free time delay compensator is implemented not only in the master side but also the slave side. The control structure has become symmetric in the master side and the slave side. Furthermore, the performance has been improved. The validity is confirmed by numerical analysis and experimental results.