Intense changes in cortical microstructure occur during early infancy. Here, we aimed to study cortical maturation over this largely unexplored developmental period using quantitative MRI in 17 infants from 1 to 5 post-natal months. By taking benefit of robust intra- and inter-individual registrations of anatomical images and parametric maps, we measured T1, T2 relaxation times, and DTI longitudinal diffusivity over cortical surfaces and regions of interest. Results showed that each parameter relevantly but differently reflects the progressive maturation. This suggests that multi-parametric approaches might provide interpretable measures of the developing microstructure by accounting for the parameters complementarity.