When the brain has determined the position of a moving object, due to anatomical and processing delays, the object will have already moved to a new location. Given the statistical regularities present in natural motion, the brain may have acquired compensatory mechanisms to minimize the mismatch between the perceived and the real position of moving objects. A well-known visual illusion — the flash lag effect — points towards such a possibility. Although many psychophysical models have been suggested to explain this illusion, their predictions have not been tested at the neural level, particularly in a species of animal known to perceive the illusion. Towards this, we recorded neural responses to flashed and moving bars from primary visual cortex (V1) of awake, fixating macaque monkeys. We found that the response latency to moving bars of varying speed, motion direction and luminance was shorter than that to flashes, in a manner that is consistent with psychophysical results. At the level of V1, our results support the differential latency model positing that flashed and moving bars have different latencies. As we found a neural correlate of the illusion in passively fixating monkeys, our results also suggest that judging the instantaneous position of the moving bar at the time of flash — as required by the postdiction/motion-biasing model — may not be necessary for observing a neural correlate of the illusion. Our results also suggest that the brain may have evolved mechanisms to process moving stimuli faster and closer to real time compared with briefly appearing stationary stimuli.