Abstract Congenital heart disease (CHD) is associated with impaired early brain development and adverse neurodevelopmental outcomes. This study investigated how individualised measures of preoperative cortical gyrification index (GI) differ in 142 infants with CHD, using a normative modelling approach with reference data from 320 typically developing infants. GI Z-scores for the whole brain and six major cortical areas were generated using two different normative models: one accounting for postmenstrual age at scan, postnatal age at scan and sex, and another additionally accounting for supratentorial brain volume (STBV). These Z-scores were compared between CHD and control groups to test the hypothesis that cortical folding in infants with CHD deviates from the normal developmental trajectory. The relationships between whole-brain GI Z-scores from the two normative models and both cerebral oxygen delivery (CDO2) and neurodevelopmental outcomes were also investigated. Global and regional brain gyrification was significantly reduced in neonates with CHD, but not when STBV was accounted for. This finding suggests that whilst cortical folding is reduced in CHD, it is primarily driven by a reduction in brain size. There was a significant positive correlation between CDO2 and whole-brain GI Z-scores in CHD, but not when STBV was accounted for. CDO2 is therefore likely to play a more important role in the biological processes underlying volumetric brain growth than cortical folding. No significant associations between whole-brain GI Z-scores and motor/cognitive outcomes or autism traits were identified in the 70 infants with CHD who underwent neurodevelopmental assessment at 22-months. Our results suggest that chronic in-utero and early postnatal hypoxia in CHD is associated with reductions in cortical folding that are proportional to reductions in supratentorial brain volume.