Little is known about the manual tracking of targets that move in three dimensions. In the present study, human subjects followed, with the tip of a hand-held pen, a virtual target moving four times (period 5 s) around a novel, unseen path. Two basic types of target paths were used: a peanut-shaped Cassini ellipse and a quasi-spherical shape where four connected semicircles lay in orthogonal planes. The quasi-spherical shape was presented in three different sizes, and the Cassini shape was varied in spatial orientation and by folding it along one of the three bend axes. During the first cycle of Cassini shapes, the hand lagged behind the target by about 150 ms on average, which decreased to 100 ms during the last three cycles. Tracking performance gradually improved during the first 3 s of the first cycle and then stabilized. Tracking was especially good during the smooth, planar sections of the shapes, and time lag was significantly shorter when the tracking of a low-frequency component was compared to performance at a higher frequency (-88 ms at 0.2 Hz vs. -101 ms at 0.6 Hz). Even after the appropriate adjustment of the virtual target path to a virtual shape tracing condition, tracking in depth was poor compared to tracking in the frontal plane, resulting in a flattening of the hand path. In contrast to previous studies where target trajectories were linear or sinusoidal, these complex trajectories may have involved estimation of the overall shape, as well as prediction of target velocity.