Research on goal-predictive gaze shifts in infancy so far has mostly focused on the effect of infants’ experience with observed actions or the effect of agency cues that the observed agent displays. However, the perspective from which an action is presented to the infants (egocentric vs. allocentric) has received only little attention from researchers despite the fact that the natural observation of own actions is always linked to an egocentric perspective, whereas the observation of others’ actions is often linked to an allocentric perspective. The current study investigated the timing of 6-, 9-, and 12-month-olds’ goal-predictive gaze behavior, as well as that of adults, during the observation of simple human grasping actions that were presented from either an egocentric or allocentric perspective (within-participants design). The results showed that at 6 and 9 months of age, the infants predicted the action goal only when observing the action from the egocentric perspective. The 12-month-olds and adults, in contrast, predicted the action in both perspectives. The results therefore are in line with accounts proposing an advantage of egocentric versus allocentric processing of social stimuli, at least early in development. This study is among the first to show this egocentric bias already during the first year of life.