Quantitative measurement of dynamic cortex development during early postnatal stages is of great importance to understand early cortical structural and functional development. Conventional methods usually independently reconstruct cortical surfaces of longitudinal images from the same infant, which often generates longitudinally-inconsistent cortical surfaces and leads to inconsistence in cortex development measurement. This paper aims to address this problem by presenting a method to reconstruct consistent cortical surfaces from longitudinal brain MR images in the first-year infants for accurate and consistent measurement of dynamic cortex development. Specifically, longitudinal development of the inner cortical surface is first modeled by a deformable sheet with elasto-plasticity property to establish longitudinally smooth correspondences of inner cortical surfaces. Then, the modeled longitudinal inner cortical surfaces are jointly deformed to locate inner and outer cortical surfaces with a spatial-temporal deformable surface. The method has been applied on 10 infants, each with 5 or 6 scans acquired at every 3 months from birth. Experimental results show that our method can accurately and consistently reconstruct dynamic cortical surfaces from longitudinal infant images, with the average surface distance as low as 0.2mm. By using our method, we can quantitatively characterize longitudinally dynamic cortical thickness development in the first-year infants.