Dispersal is a major determinant of the dynamics and genetic structure of populations, and its consequences depend not only on average dispersal rates and distances, but also on the characteristics of dispersing and philopatric individuals. We investigated whether natal dispersal correlated with a predisposed behavioural trait: exploratory behaviour in novel environments. Wild great tits were caught in their natural habitat, tested the following morning in the laboratory using an open field test and released at the capture site. Natal dispersal correlated positively with parental and individual exploratory behaviour, using three independent datasets. First, fast–exploring parents had offspring that dispersed furthest. Second, immigrants were faster explorers than locally born birds. Third, post–fledging movements, comprising a major proportion of the variation in natal dispersal distances, were greater for fast females than for slow females. These findings suggest that parental behaviour influenced offspring natal dispersal either via parental behaviour per se (e.g. via post–fledging care) or by affecting the phenotype of their offspring (e.g. via their genes). Because this personality trait has a genetic basis, our results imply that genotypes differ in their dispersal distances. Therefore, the described patterns have profound consequences for the genetic composition of populations.