Background: Despite the limited evidence, accelerated early postnatal growth (EPG) is commonly believed to benefit neurodevelopment for term-born infants, especially those small for gestational age. Objectives: To investigate the existence of critical time windows in the association of EPG with neurodevelopment, considering birth size groups. Study design: In the French ELFE birth cohort, 12,854 term-born neonates were classified as small, appropriate or large for gestational age (SGA, AGA, LGA, respectively). Parents reported their child's development by using the Child Development Inventory (CDI-score) at age 12 months and the MacArthur-Bates Development Inventory (MAB-score; 100 score units) assessing language ability at age 24 months. Predictions of individual weight, body mass index (BMI), length, and head circumference (HC) from birth to age 24 months were obtained from repeated measurements fitted with the Jenss-Bayley mixed-effects model. For each infant, conditional gains (CG) in these growth parameters were generated at four-time points (3, 6, 12 and 24 months) representing specific variations in growth parameters during 0-3, 3-6, 6-12, 12-24 months, independent of previous measures. Using multivariable linear regression models, we provided the estimate differences of the neurodevelopmental scores according to variation of each growth parameter CG, by birth size group. Results: For SGA infants, the MAB-score differed by 5.8 (95% confidence interval [CI] -0.2, 11.8), 6.7 (95% CI -0.1, 13.3), and 9.7 (95% CI 1.9, 17.5) score units when CG in BMI, weight, and HC at 3 months varied from -2 to 1 standard deviation, respectively. For all infants, MAB-score was linearly and positively associated with length conditional gains at 12 months, with stronger magnitude for SGA infants. Results for the CDI-score were overall consistent with those for MAB-score. Conclusions: For term-born SGA infants, moderate catch-up in HC, BMI and weight within the first 3 months of life may benefit later neurodevelopment, which could guide clinicians to monitor EPG.