Structural covariance assesses similarities in gray matter between brain regions and can be applied to study networks of the brain. In this study, we explored correlations between structural covariance networks (SCNs) and cognitive impairment in Parkinson’s disease patients. 101 PD patients and 58 age- and sex-matched healthy controls were enrolled in the study. For each participant, comprehensive neuropsychological testing using the Wechsler Adult Intelligence Scale-III and Cognitive Ability Screening Instrument were conducted. Structural brain MR images were acquired using a 3.0T whole body GE Signa MRI system. T1 structural images were preprocessed and analyzed using Statistical Parametric Mapping software (SPM12) running on Matlab R2016a for voxel-based morphometric analysis and SCN analysis. PD patients with normal cognition received follow-up neuropsychological testing at 1-year interval. Cognitive impairment in PD is associated with degeneration of the amygdala/hippocampus SCN. PD patients with dementia exhibited increased covariance over the prefrontal cortex compared to PD patients with normal cognition (PDN). PDN patients who had developed cognitive impairment at follow-up exhibited decreased gray matter volume of the amygdala/hippocampus SCN in the initial MRI. Our results support a neural network-based mechanism for cognitive impairment in PD patients. SCN analysis may reveal vulnerable networks that can be used to early predict cognitive decline in PD patients.