The present study asks when infants are able to selectively anticipate the goals of observed actions, and how this ability relates to infants’ own abilities to produce those specific actions. Using eye-tracking technology to measure on-line anticipation, 6-, 8- and 10-month-old infants and a control group of adults were tested while observing an adult reach with a whole hand grasp, a precision grasp or a closed fist towards one of two different sized objects. The same infants were also given a comparable action production task. All infants showed proactive gaze to the whole hand grasps, with increased degrees of proactivity in the older groups. Gaze proactivity to the precision grasps, however, was present from 8 months of age. Moreover, the infants’ ability in performing precision grasping strongly predicted their ability in using the actor’s hand shape cues to differentially anticipate the goal of the observed action, even when age was partialled out. The results are discussed in terms of the specificity of action anticipation, and the fine-grained relationship between action production and action perception.