We propose a quantitative model for human smooth pursuit tracking of a continuously moving visual target which is based on synchronization of an internal expectancy model of the target position coupled to the retinal target signal. The model predictions are tested in a smooth circular pursuit eye tracking experiment with transient target blanking of variable duration. In subjects with a high tracking accuracy, the model accounts for smooth pursuit and repeatedly reproduces quantitatively characteristic patterns of the eye dynamics during target blanking. In its simplest form, the model has only one free parameter, a coupling constant. An extended model with a second parameter, a time delay or memory term, accounts for predictive smooth pursuit eye movements which advance the target. The model constitutes an example of synchronization of a complex biological system with perceived sensory signals.