Purpose: This study focuses on the asymptomatic neurocognitive impairment (ANI) stage of HIV-associated neurocognitive disorders (HAND). Using multimodal MRI and large-scale brain network analysis, we aimed to investigate alterations in functional networks, structural networks, and functional-structural coupling in persons with ANI. Patients and Methods: A total of 95 participants, including 48 healthy controls and 47 persons with HIV-ANI, were enrolled. Resting-state fMRI and diffusion tensor imaging were used to construct functional and structural connectivity matrices. Graph-theoretical analysis was employed to assess inter-group differences in global metrics, nodal characteristics, and functional-structural coupling patterns. Furthermore, machine learning classifiers were used to construct and evaluate classification models based on imaging features from both groups. The performance of different models was compared to identify the optimal diagnostic model for detecting HIV-ANI. Results: Structural network analysis showed no significant changes in the global or local topological properties of persons with ANI. In contrast, functional networks exhibited significant reorganization in key regions, including the visual, executive control, and default mode networks. Functional-structural coupling was significantly enhanced in the occipital and frontal networks. These changes correlated with immune status, infection duration, and cognitive performance. Furthermore, the classification model integrating graph-theoretical topological features and functional connectivity achieved the best performance, with an area under the curve (AUC) of 0.962 in the test set. Conclusion: Functional network reorganization and enhanced functional-structural coupling may reflect early synaptic and dendritic damage in persons with ANI, serving as potential early warning signals for HAND progression. These findings provide sensitive biomarkers and valuable perspectives for early diagnosis and intervention.