Accelerated growth in postnatal life in low birth weight infants has been associated with insulin resistance and metabolic syndrome-related disorders in later life. Postnatal accelerated growth in also common in normal birth weight infants, but little is known about the impact on metabolic health. In a prospective cohort study of 203 term normal birth weight infants, we evaluated the impacts of accelerated (Δweight Z score > 0.5) or decelerated (Δweight ΔZ < −0.5) growth during early (0–3 months) and late (3–12 months) postnatal life on metabolic health indicators at age 1-year. The primary outcomes were homeostasis model assessment of insulin resistance (HOMA-IR), β-cell function [homeostasis model assessment of β-cell function (HOMA-β)], and fasting plasma lipids. Adjusting for maternal, paternal, and infant characteristics, accelerated growth during the first 3 months of life was associated with a 41.6% (95% confidence interval 8.9–84.2%) increase in HOMA-β, and a 8.3% (0.7–15.4%) decrease in fasting plasma total cholesterols, and was not associated with HOMA-IR in infants at age 1-year. Accelerated growth during 3–12 months was associated with a 30.9% (3.3–66.0%) increase in HOMA-IR and was not associated with HOMA-β. Neither accelerated nor decelerated growth was associated with fasting plasma triglycerides, high-density lipoprotein or low-density lipoprotein cholesterol concentrations in infants at age 1-year. Accelerated growth during early postnatal life may be beneficial for β-cell function, but during late postnatal life harmful for insulin sensitivity in normal birth weight infants.