Widespread structural changes have been observed in patients with stroke in previous diffusion tensor imaging studies. However, the topological organization of white matter structural networks after acute ischemic stroke (AIS) in the right basal ganglia (BG) remains unknown. The aim of our study is to investigate whether the topological structure of the white matter structural network is altered in patients with AIS in the right BG, and its relationship with cognition. Graph theoretical analysis was employed to investigate the topological architecture of whole-brain white matter structural networks in 40 AIS patients in the right BG and 40 healthy controls (HC), and network-based statistics (NBS) were applied to examine structural connectivity alterations. Compared to HC, AIS patients exhibited altered global network properties characterized by increased small-worldness, normalized clustering coefficient, and shortest path length, as well as decreased clustering coefficient, local efficiency, and global efficiency. The nodes with significantly decreased nodal properties in AIS patients were primarily located in the default mode network, limbic system, sensorimotor system, salience network, and central executive network. Reduced structural connectivity detected by NBS in AIS patients were primarily located in the lesional hemisphere. Furthermore, altered nodal properties were correlated with cognitive scores. Documenting the alterations in the topological patterns of white matter structural networks will help to promote the understanding of the neural mechanisms of cognitive impairment after AIS in the right BG.