We propose a method for constructing a spatio-temporal cortical surface atlas of neonatal brains aged between 36 and 44 weeks of post-menstrual age (PMA) at the time of scan. The data were acquired as part of the Developing Human Connectome Project (dHCP), and the constructed surface atlases are publicly available. The method is based on a spherical registration approach: Multimodal Surface Matching (MSM), using cortical folding for driving the alignment. Templates have been generated for the anatomical cortical surface and for the cortical feature maps: sulcal depth, curvature, thickness, T1w/T2w myelin maps and cortical regions. To achieve this, cortical surfaces from 270 infants were first projected onto the sphere. Templates were then generated in two stages: first, a reference space was initialised via affine alignment to a group average adult template. Following this, templates were iteratively refined through repeated alignment of individuals to the template space until the variability of the average feature sets converged. Finally, bias towards the adult reference was removed by applying the inverse of the average affine transformations on the template and de-drifting the template. We used temporal adaptive kernel regression to produce age-dependant atlases for 9 weeks (36–44 weeks PMA). The generated templates capture expected patterns of cortical development including an increase in gyrification as well as an increase in thickness and T1w/T2w myelination with increasing age.