The risk of neurodevelopmental disorders in low birth weight (LBW) infants has gained recognition but remains debatable. We investigated the risk of attention-deficit/hyperactivity disorder (ADHD) and autism spectrum disorder (ASD) in school-aged children according to their birth weight. We conducted a retrospective cohort study using the Korean National Health Insurance claims data of 2,143,652 children who were born between 2008 and 2012. Gestational age of infants was not available; thus, outcomes were not adjusted with it. Not only infants with birth weights of < 1.5 kg, but also 2.0–2.4 kg and 1.5–1.9 kg were associated with having ADHD; odds ratio (OR), 1.41 (95% confidence interval [CI] 1.33–1.50), and 1.49 (95% CI 1.33–1.66), respectively. The OR in infants with birth weights of 2.0–2.4 kg and 1.5–1.9 kg was 1.91 (95% CI 1.79–2.05) and 3.25 (95% CI 2.95–3.59), respectively, indicating increased odds of having ASD. Subgroup analysis for children without perinatal diseases showed similar results. In this national cohort, infants with birth weights of < 2.5 kg were associated with ADHD and ASD, regardless of perinatal history. Children born with LBW need detailed clinical follow-up.