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We investigated the association between poststroke cognitive impairment and a specific effective network connectivity in the prefrontal–basal ganglia circuit. The resting-state effective connectivity of this circuit was modeled by employing spectral dynamic causal modeling in 11 poststroke patients with cognitive impairment (PSCI), 8 poststroke patients without cognitive impairment (non-PSCI) at baseline and 3-month follow-up, and 28 healthy controls. Our results showed that different neuronal models of effective connectivity in the prefrontal–basal ganglia circuit were observed among healthy controls, non-PSCI, and PSCI patients. Additional connected paths (extra paths) appeared in the neuronal models of stroke patients compared with healthy controls. Moreover, changes were detected in the extra paths of non-PSCI between baseline and 3-month follow-up poststroke, indicating reorganization in the ipsilesional hemisphere and suggesting potential compensatory changes in the contralesional hemisphere. Furthermore, the connectivity strengths of the extra paths from the contralesional ventral anterior nucleus of thalamus to caudate correlated significantly with cognitive scores in non-PSCI and PSCI patients. These suggest that the neuronal model of effective connectivity of the prefrontal–basal ganglia circuit may be sensitive to stroke-induced cognitive decline, and it could be a biomarker for poststroke cognitive impairment 3 months poststroke. Importantly, contralesional brain regions may play an important role in functional compensation of cognitive decline.