This letter proposes an adaptive neural network synchronous tracking control strategy that can be suitable for event-triggered mechanism in response to the modeling uncertainties and communication delays in bilateral teleoperation systems. Through introducing the event-triggered mechanism with the aim of reducing the network communication frequency in teleoperation system, the leader and follower robots communicate with each other only when the triggering conditions are fulfilled, which enhances the efficiency of the network communication. This control strategy can guarantee the exponential convergence of the position synchronization tracking error of the leader-follower robot end-effector. Moreover, the event-triggered conditions do not require any empirical design, but can be derived inversely with the aid of the Lyapunov stability theory. And the triggering time interval between two neighboring events is verified to be non-zero. It is demonstrated by utilizing the Lyapunov principle that the presented adaptive neural network control strategy ensures the final asymptotic convergence and exponential convergence of the position synchronization tracking error for leader-follower robots under the designed event-triggered mechanisms. Eventually, the feasibility and effectiveness of the developed control strategy are validated by comparative cases.