Suicide ideation (SI) is a most high-risk clinical sign for major depressive disorder (MDD). However, whether the rich-club network organization as a core structural network is associated with SI and how the related neural circuits are distributed in MDD patients remain unknown. Total 177 participants including 69 MDD patients with SI (MDDSI), 58 MDD without SI (MDDNSI) and 50 cognitively normal (CN) subjects were recruited and completed neuropsychological tests and diffusion-tensor imaging scan. The rich-club organization was identified and the global and regional topological properties of structural networks, together with the brain connectivity of specific neural circuit architectures, were analyzed. Further, the support vector machine (SVM) learning was applied in classifying MDDSI or MDDNSI from CN subjects. MDDSI and MDDNSI patients both exhibited disrupted rich-club organizations. However, MDDSI patients showed that the differential network was concentrated on the non-core low-level network and significantly destroyed betweeness centrality was primarily located in the regional non-hub regions relative to MDDNSI patients. The differential structural network connections involved the superior longitudinal fasciculus and the corpus callosum were incorporated in the cognitive control circuit and default mode network. Finally, the feeder serves as a potentially powerful indicator for distinguishing MDDSI patients from MDDNSI or CN subjects. The altered rich-club organization provides new clues to understand the underlying pathogenesis of MDD patients, and the feeder was useful as a diagnostic neuroimaging biomarker for differentiating MDD patients with or without SI.