Among the cognitive symptoms that are associated with Parkinson's disease (PD), alterations in cognitive action control (CAC) are commonly reported in patients. CAC enables the suppression of an automatic action, in favor of a goal-directed one. The implementation of CAC is time-resolved and arguably associated with dynamic changes in functional brain networks. However, the electrophysiological functional networks involved, their dynamic changes, and how these changes are affected by PD, still remain unknown. In this study, to address this gap of knowledge, 10 PD patients and 10 healthy controls (HC) underwent a Simon task while high-density electroencephalography (HD-EEG) was recorded. Source-level dynamic connectivity matrices were estimated using the phase-locking value in the beta (12-25 Hz) and gamma (30-45 Hz) frequency bands. Temporal independent component analyses were used as a dimension reduction tool to isolate the task-related brain network states. Typical microstate metrics were quantified to investigate the presence of these states at the subject-level. Our results first confirmed that PD patients experienced difficulties in inhibiting automatic responses during the task. At the group-level, we found three functional network states in the beta band that involved fronto-temporal, temporo-cingulate and fronto-frontal connections with typical CAC-related prefrontal and cingulate nodes (e.g., inferior frontal cortex). The presence of these networks did not differ between PD patients and HC when analyzing microstates metrics, and no robust correlations with behavior were found. In the gamma band, five networks were found, including one fronto-temporal network that was identical to the one found in the beta band. These networks also included CAC-related nodes previously identified in different neuroimaging modalities. Similarly to the beta networks, no subject-level differences were found between PD patients and HC. Interestingly, in both frequency bands, the dominant network at the subject-level was never the one that was the most durably modulated by the task. Altogether, this study identified the dynamic functional brain networks observed during CAC, but did not highlight PD-related changes in these networks that might explain behavioral changes. Although other new methods might be needed to investigate the presence of task-related networks at the subject-level, this study still highlights that task-based dynamic functional connectivity is a promising approach in understanding the cognitive dysfunctions observed in PD and beyond.