This study explored how the human cortical folding pattern composed of convex gyri and concave sulci affected single-subject morphological brain networks, which are becoming an important method for studying the human brain connectome. We found that gyri-gyri networks exhibited higher morphological similarity, lower small-world parameters, and lower long-term test-retest reliability than sulci-sulci networks for cortical thickness- and gyrification index-based networks, while opposite patterns were observed for fractal dimension-based networks. Further behavioral association analysis revealed that gyri-gyri networks and connections between gyral and sulcal regions significantly explained inter-individual variance in Cognition and Motor domains for fractal dimension- and sulcal depth-based networks. Finally, the clinical application showed that only sulci-sulci networks exhibited morphological similarity reductions in major depressive disorder for cortical thickness-, fractal dimension-, and gyrification index-based networks. Taken together, these findings provide novel insights into the constraint of the cortical folding pattern to the network organization of the human brain.