Neural substrates for processing constant speed visual motion have been extensively studied. Less is known about the brain activity patterns when the target speed changes continuously, for instance under the influence of gravity. Using functional MRI (fMRI), here we compared brain responses to accelerating/decelerating targets with the responses to constant speed targets. The target could move along the vertical under gravity (1g), under reversed gravity (-1g), or at constant speed (0g). In the first experiment, subjects observed targets moving in smooth motion and responded to a GO signal delivered at a random time after target arrival. As expected, we found that the timing of the motor responses did not depend significantly on the specific motion law. Therefore brain activity in the contrast between different motion laws was not related to motor timing responses. Average BOLD signals were significantly greater for 1g targets than either 0g or -1g targets in a distributed network including bilateral insulae, left lingual gyrus, and brain stem. Moreover, in these regions, the mean activity decreased monotonically from 1g to 0g and to -1g. In the second experiment, subjects intercepted 1g, 0g, and -1g targets either in smooth motion (RM) or in long-range apparent motion (LAM). We found that the sites in the right insula and left lingual gyrus, which were selectively engaged by 1g targets in the first experiment, were also significantly more active during 1g trials than during -1g trials both in RM and LAM. The activity in 0g trials was again intermediate between that in 1g trials and that in -1g trials. Therefore in these regions the global activity modulation with the law of vertical motion appears to hold for both RM and LAM. Instead, a region in the inferior parietal lobule showed a preference for visual gravitational motion only in LAM but not RM.