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Background: To examine whether the patterns of head-size growth trajectory in the first month after birth are associated with different susceptibility to cognitive impairment outcomes at age 24 months. Methods: This retrospective cohort study included 590 infants of very-preterm survivors born between 2001 and 2016 receiving neurodevelopmental assessment at age 24 months. 403 children were enrolled for analysis after excluding infants with small-for-gestational age and severe brain injury. The head circumference (HC) growth evaluated weekly in the first month after birth compared to the at-birth HC was analyzed using group-based trajectory modeling. Neurocognition outcomes were determined as normal, borderline delay, or impaired using the Bayley Scales of Infant Development. Results: The HC growth dynamics in the first month after birth showed three trajectory patterns: delayed catch-up (31.5%), slow catch-up (54.0%), and fast catch-up (14.5%), which significantly corresponded to different rates of impaired cognition at 19.5%, 6.0%, and 8.5%, respectively (p < 0.001). While 60% of the fast catch-up group had normal cognition, only one-third of the delayed catch-up group showed normal cognition. Three neonatal risk factors, gestational age (p = 0.006), respiratory distress syndrome requiring surfactant therapy (p = 0.012), and hemodynamically significant patent ductus arteriosus requiring intervention (p = 0.047) significantly affected HC growth trajectory patterning that led to cognitive impairment outcomes at follow-up. Conclusion: Preterm infants with delayed catch-up of head-size growth in the first month of age is susceptible to cognitive impairment outcome.