Many industry applications of teleoperating cyber-physical system (TCPS) require operator and slave to keep state synchronization on the shared information. However, the cyber-constrained property of TCPS makes it challenging to achieve such a synchronization. This paper is concerned with a state synchronization problem for TCPS, subjected to time-varying communication delay in cyber channels. A proportional-derivative (PD) controller with dynamic gains is designed to enforce the state synchronization of master and slave robots. Particularly, the gains are in the form of incremental rates, which can be dynamically adjusted by the delayed inputs. By introducing an appropriate state transformation, the dynamics of master and slave robots are rearranged as port-Hamiltonian systems, through which the state synchronization is converted into a stabilization problem of the augmented system. Meanwhile, stability conditions are given to show that the proposed synchronization controller can stabilize the closed-loop TCPS. Finally, simulation and experiment results are performed to show the validity of our proposed method. It is demonstrated that the adjustable gain-based synchronization controller can improve the dynamic and steady-state performance of TCPS by comparing with the traditional PD controllers.