The current study investigated how individual differences among children affect the added value of social robots for teaching second language (L2) vocabulary to young children. Specifically, we investigated the moderating role of three individual child characteristics deemed relevant for language learning: first language (L1) vocabulary knowledge, phonological memory, and selective attention. We expected children low in these abilities to particularly benefit from being assisted by a robot in a vocabulary training. An L2 English vocabulary training intervention consisting of seven sessions was administered to 193 monolingual Dutch five-year-old children over a three- to four-week period. Children were randomly assigned to one of three experimental conditions: 1) a tablet only, 2) a tablet and a robot that used deictic (pointing) gestures (the no-iconic-gestures condition), or 3) a tablet and a robot that used both deictic and iconic gestures (i.e., gestures depicting the target word; the iconic-gestures condition). There also was a control condition in which children did not receive a vocabulary training, but played dancing games with the robot. L2 word knowledge was measured directly after the training and two to four weeks later. In these post-tests, children in the experimental conditions outperformed children in the control condition on word knowledge, but there were no differences between the three experimental conditions. Several moderation effects were found. The robot's presence particularly benefited children with larger L1 vocabularies or poorer phonological memory, while children with smaller L1 vocabularies or better phonological memory performed better in the tablet-only condition. Children with larger L1 vocabularies and better phonological memory performed better in the no-iconic-gestures condition than in the iconic-gestures condition, while children with better selective attention performed better in the iconic-gestures condition than the no-iconic-gestures condition. Together, the results showed that the effects of the robot and its gestures differ across children, which should be taken into account when designing and evaluating robot-assisted L2 teaching interventions.