Subjects made fast goal-directed arm movements towards moving targets. In some cases, the perceived direction of target motion was manipulated by moving the background. By comparing the trajectories towards moving targets with those towards static targets, we determined the position towards which subjects were aiming at movement onset. We showed that this position was an extrapolation in the target's perceived direction from its position at that moment using its perceived direction of motion. If subjects were to continue to extrapolate in the perceived direction of target motion from the position at which they perceive the target at each instant, the error would decrease during the movements. By analysing the differences between subjects' arm movements towards targets moving in different (apparent) directions with a linear second-order model, we show that the reduction in the error that this predicts is not enough to explain how subjects compensate for their initial misjudgements.