Consistent behavioural differences among individuals are common in many species and can have important effects on offspring fitness. To understand such ‘personality’ variation, it is important to determine the mode of inheritance, but this has been quantified for only a few species. Here, we report results from a breeding experiment in captive zebra finches, Taeniopygia guttata, in which we cross-fostered offspring to disentangle the importance of genetic and non-genetic transmission of behaviour. Genetic and foster-parents’ exploratory type was measured in a novel environment pre-breeding and offspring exploratory type was assessed at adulthood. Offspring exploratory type was predicted by the exploratory behaviour of the foster but not the genetic parents, whereas offspring size was predicted by genetic but not foster-parents’ size. Other aspects of the social environment, such as rearing regime (uni- versus biparental), hatching position, brood size or an individual's sex did not influence offspring exploration. Our results therefore indicate that non-genetic transmission of behaviour can play an important role in shaping animal personality variation.