Individuals in the vanguard of a species invasion face altered selective conditions when compared with conspecifics behind the invasion front. Assortment by dispersal ability on the expanding front, for example, drives the evolution of increased dispersal, which, in turn, leads to accelerated rates of invasion. Here I propose an additional evolutionary mechanism to explain accelerating invasions: shifts in population growth rate (r). Because individuals in the vanguard face lower population density than those in established populations, they should (relative to individuals in established populations) experience greater r-selection. To test this possibility, I used the ongoing invasion of cane toads (Bufo marinus) across northern Australia. Life-history theory shows that the most efficient way to increase the rate of population growth is to reproduce earlier. Thus, I predict that toads on the invasion front will exhibit faster individual growth rates (and thus will reach breeding size earlier) than those from older populations. Using a common garden design, I show that this is indeed the case: both tadpoles and juvenile toads from frontal populations grow around 30 per cent faster than those from older, long established populations. These results support theoretical predictions that r increases during range advance and highlight the importance of understanding the evolution of life history during range advance.