The reasons why not all stroke survivors have cognitive dysfunction are unclear. We hypothesize that resting-state fMRI (rs-fMRI) will reveal differences in regional brain spontaneous activity and functional connectivity (FC) in stroke patients with and without cognitive impairment. We classified 62 first-ever non-acute subcortical stroke patients into two groups: post-stroke with abnormal cognition (PSAC) and with normal cognition (PSNC). Rs-MRI was utilized to assess regional homogeneity (ReHo) in 32 PSAC, 30 PSNC, and 62 age- and sex-matched healthy controls. We set regions with significant alteration within stroke groups as regions of interest and performed the seed-based whole brain FC analysis. A partial correlation analysis examined the relationship between altered ReHo or FC and Montreal Cognitive Assessment (MoCA) scores. Compared to PSNC, PSAC had decreased ReHo in the left gyrus rectus (REC) and increased ReHo in cerebellar lobules (CBL) left IX and right VIII, while FC decreased in PSAC between bilateral REC, and between the left REC and the middle temporal gyrus (MTG). In all stroke patients, ReHo value in the left REC correlated positively and in the CBL correlated negatively with MoCA. All the significant FC correlated with MoCA positively. Regional brain spontaneous activity and FC alteration in the REC, MTG, and cerebellum may be associated with cognitive impairment following non-acute subcortical stroke.