The human brain is thought to respond differently to novel versus predictable neural input. In human visual cortex, neural response amplitude to visual input might be determined by the degree of predictability. We investigated how fMRI BOLD responses in human early visual cortex reflect the anticipation of a single moving bar's trajectory. We found that BOLD signals decreased linearly from onset to offset of the stimulus trajectory. Moreover, decreased amplitudes of BOLD responses coincided with an increased initial dip as the stimulus moved along its trajectory. Importantly, motion anticipation effects were absent, when motion coherence was disrupted by means of stimulus contrast reversals. These results show that human early visual cortex anticipates the trajectory of a coherently moving object at the initial stages of visual motion processing. The results can be explained by suppression of predictable input, plausibly underlying the formation of stable visual percepts.