A synchronization control method is proposed for nonlinear teleoperation systems with dynamic uncertainty, time-varying delay and input saturation. Time delay estimation (TDE) is utilized to estimate the dynamic uncertainty including the parametric uncertainty and unknown disturbance. A hyperbolic tangent saturation function with adjustable factor is designed to restrict the control input saturation and make the control input smoother at the critical saturation threshold. Further, the estimated value obtained from TDE is introduced into a PD-like controller to derive the position synchronization controller. The stability and convergence of the system is proved via Lyapunov function. It is experimentally verified that the synchronization control method can restrict the control input within the saturation threshold. Besides, the position tracking error is able to converge quickly under time-varying delay.