Early childhood growth is associated with cognitive function. However, the independent associations of fat mass (FM) and fat-free mass (FFM) with cognitive function are not well understood. We investigated associations of FM and FFM at birth and 0-5 years accretion with cognitive function at 10 years. Healthy term newborns were enrolled in this cohort. FM and FFM were measured at birth, 1.5, 2.5, 3.5, 4.5, 6 months, 4 and 5 years. Cognitive function was assessed using Peabody Picture Vocabulary Test (PPVT) at 10 years. FM and FFM accretion were computed using statistically independent conditional accretion from 0-3 months, 3-6 months, 6 months-4 years, and 4-5 years. Multiple linear regression was used to assess associations. At the 10-year follow-up, we assessed 318 children with mean (SD) age of 9.8 (1.0) years. A 1 SD higher birth FFM was associated with a 0.14 SD (95% CI: 0.01, 0.28) higher PPVT at 10 years. FFM accretion from 0-3 and 3-6 months was associated with PPVT at 10 year, β = 0.5 SD (95% CI: 0.08, 0.93) and β = -0.48 SD (95% CI: -0.90, -0.07, respectively. FFM accretion after 6 months showed no association with PPVT. Neither FM at birth nor 0-5 years accretion showed association with PPVT. Overall, birth FFM, but not FM was associated with cognitive function at 10 years, while the association of FFM accretion and cognitive function varied across distinct developmental stages in infancy. The mechanisms underlying this varying association between body composition and cognitive function need further investigation.