Parkinson’s disease (PD) is a neurodegenerative disease that leads to memory impairment and executive and visuospatial dysfunction as the disease progresses. Alpha activity on EEG has been related to cognition in previous studies. We aimed to investigate the correlation between alpha activity and neuropsychometric tests (NPTs) in PD patients. Fifty-five idiopathic PD patients and 20 healthy controls were included. The Standardized Mini-Mental Test (SMMT), Verbal Learning Memory Test (VLMT), Wechsler Memory Scale (WMS), Stroop Color–Word Test, Categorical Verbal Fluency Test (CVFT), Benton’s Face Recognition Test (BFR), and Benton Line Judgment Orientation Test (BLOT) were administered to all participants. Patients were separated into four groups according to NPT results: healthy controls (HC); PD patients with normal cognition (PDNC); PD patients with MCI (PDMCI); and PD patients with dementia (PDD). Analysis of the EEG data showed that HC had the highest alpha activity, and PDD had the lowest. High SMMT scores were correlated with high alpha activity at posterior electrode locations in all PD groups. VLMT and WMS test scores were associated with alpha activity at the parietal sites in PDMCI. VLMT, WMS, and CVFT test scores were correlated with alpha activity at parietooccipital sites in PDD. Verbal and visuospatial memory dysfunction related to low alpha activity was evident in both PDMCI and PDD, whereas executive dysfunction was more strongly associated with low alpha activity in PDD. Analysis of alpha activity could help clinicians predict the progression of cognitive dysfunction in PD patients.