To evaluate the relative importance of overall and period-specific postnatal growth and their interaction with fetal growth on cognition in a generally well-nourished population. We included 1052 children from Project Viva, a prospective cohort in Boston, Massachusetts. Using linear spline mixed-effects models, we modeled length/height and body mass index (BMI) trajectories from birth to 7years and estimated standardized overall (0-7years) and period-specific growth velocities ie, early infancy (0-4months), late infancy (4-15months), toddlerhood (15-37months), and early childhood (37-84months). We investigated associations of growth velocities as well as their interactions with birthweight-for-gestational age on mid-childhood (mean age: 7.9years) IQ, visual memory and learning, and visual motor ability. Greater overall height velocity was associated with modestly higher design memory score, (adjusted β [95% CI] 0.19 [-0.01,0.38] P=.057])points per SD increase but lower verbal IQ (-0.88 [-1.76,0.00] P=.051). Greater early infancy height velocity was associated with higher visual motor score (1.92 [0.67,3.18]). Greater overall BMI velocity was associated with lower verbal IQ (-0.71 [-1.52,0.11] P=.090). Greater late infancy BMI velocity was associated with lower verbal IQ (-1.21 [-2.07,-0.34]), design memory score (-0.22 [-0.42,-0.03)], but higher picture memory score (0.22 [0.01,0.43]). Greater early infancy height velocity (-1.5 SD vs 1.5 SD) was associated with higher nonverbal IQ (margins [95% CI] 102.6 [98.9106.3] vs 108.2 [104.9111.6]) among small-for-gestational age infants (P-interaction=0.04). Among generally well-nourished children, there might not be clear cognitive gains with faster linear growth except for those with lower birthweight-for-gestational age, revealing the potential importance of early infancy compensatory growth.