Escaped transgenic organisms (GMO’s) may threaten the populations of their wild relatives if able to hybridize with each other. The introgression of a growth enhancement transgene into a wild Atlantic salmon population may be affected by the transgene’s effects not only on fitness parameters, but also on mating behaviour. Large anadromous GMO males are most preferred in mating, but a transgene can also give the large sneakers a reproductive advantage over the smaller wild individuals. With a simulation model, we studied whether the increase in the proportion and mating success of sneakers in transgenic and hybrid genotypes could facilitate the introgression of a transgene into wild population after the release of GMOs. The model combines population dynamics and Mendelian inheritance of a transgenic trait. We found that the introgression of the transgene is strongly affected by the greater mating preference of large GMO males. Furthermore, the difference in reproductive success between the anadromous versus sneaker strategy defines how much GMO’s have to be preferred to be able to invade. These results emphasize the importance of detailed knowledge of reproductive systems and the effect of a transgene on the phenotype and behaviour of GMOs when assessing the consequences of their release or escape to the wild.