Preterm-born neonates are prone to impaired neurodevelopment that may be associated with disrupted whole-brain structural connectivity. The present study aimed to investigate the longitudinal developmental pattern of the structural network from preterm birth to term-equivalent age (TEA), and identify how prematurity influences the network topological organization and properties of local brain regions. Multi-shell diffusion-weighted MRI of 28 preterm-born scanned a short time after birth (PB-AB) and at TEA (PB-TEA), and 28 matched term-born (TB) neonates in the Developing Human Connectome Project (dHCP) were used to construct structural networks through constrained spherical deconvolution tractography. Structural network development from preterm birth to TEA showed reduced shortest path length, clustering coefficient, and modularity, and more "connector" hubs linking disparate communities. Furthermore, compared with TB newborns, premature birth significantly altered the nodal properties (i.e., clustering coefficient, within-module degree, and participation coefficient) in the limbic/paralimbic, default-mode, and subcortical systems but not global topology at TEA, and we were able to distinguish the PB from TB neonates at TEA based on the nodal properties with 96.43% accuracy. Our findings demonstrated a topological reorganization of the structural network occurs during the perinatal period that may prioritize the optimization of global network organization to form a more efficient architecture; and local topology was more vulnerable to premature birth-related factors than global organization of the structural network, which may underlie the impaired cognition and behavior in PB infants.