Do children with lower test scores benefit more from breastfeeding than those with higher scores? In this paper, I examine the distributional effects of maternal breastfeeding on the cognitive test scores of 11,544 children who were born in 2000 and 2001 in the United Kingdom using a semiparametric quantile regression model. I find evidence that maternal breastfeeding has larger positive impacts on children with lower test scores. Effects for children below the 20th percentile are about 2-2.5 times greater than those for children above the 80th percentile. I also find that these distributional effects are larger when the duration of breastfeeding is extended. One policy implication is that a public policy aims at promoting breastfeeding might narrow a disparity in children's cognition.