Humans have an anisotropic perception of motion in depth. An object moving towards the eye is perceived correctly, but when an object is moving away the points closest to the eye appear to be moving faster than the points further away from the eye. This research examined if there is a difference between eye movement patterns during the two directions (forwards and away), how the eye tracks an accelerating or decelerating target, and if the anisotropic response to motion can be improved with practice. Participants were asked to watch a movie of a target moving across a computer screen. The target moved either left to right accelerating from a slow velocity (forwards condition), or right to left decelerating from a fast velocity (backwards condition). Participant’s eye velocity and saccades were used to look for differences between the two conditions as well as changes over time (learning). It was found that mean tracking velocity errors differed between the directions, and at different time slices of the videos. Participants learned to make less tracking errors at the highest velocities during the backwards condition. Anticipation differed between the directions, as anticipation was only seen during the backwards condition. Participants learned to make saccades prior to the motion of the target, and the more trials they experienced the greater the learning results. Overall, a number of differences were identified between accelerating and decelerating movement conditions indicating that eye movements may play a role in the anisotropic perception of motion in depth effect.