Analysis of anatomical covariance for cortex morphology in individual subjects plays an important role in the study of human brains. However, the approaches for constructing individual structural networks have not been well developed yet. Existing methods based on patch-wise image intensity similarity suffer from several major drawbacks, i.e., 1) violation of cortical topological properties, 2) sensitivity to intensity heterogeneity, and 3) influence by patch size heterogeneity. To overcome these limitations, this paper presents a novel cortical surface-based method for constructing individual structural networks. Specifically, our method first maps the cortical surfaces onto a standard spherical surface atlas and then uniformly samples vertices on the spherical surface as the nodes of the networks. The similarity between any two nodes is computed based on the biologically-meaningful cortical attributes (e.g., cortical thickness) in the spherical neighborhood of their sampled vertices. The connection between any two nodes is established only if the similarity is larger than a user-specified threshold. Through leveraging spherical cortical surface patches, our method generates biologically-meaningful individual networks that are comparable across ages and subjects. The proposed method has been applied to construct cortical-thickness networks for 73 healthy infants, with each infant having two MRI scans at 0 and 1 year of age. The constructed networks during the two ages were compared using various network metrics, such as degree, clustering coefficient, shortest path length, small world property, global efficiency, and local efficiency. Experimental results demonstrate that our method can effectively construct individual structural networks and reveal meaningful patterns in early brain development.