Background Parkinson’s disease is the second most common neurodegenerative disorder with complex and distributed motor and non-motor symptoms. In this study, cortical gray matter (GM) and cerebral white matter (WM) overall atrophy, and asymmetry of atrophy are investigated in PD with normal cognitive function. Method Forty-eight male Parkinson’s disease(PD) patients with normal cognitive precede (PD-NC), and thirty matched healthy control (HC) subjects were selected from the Parkinson’s Progression Markers Initiative (PPMI) database. Brain structures volumes were extracted using Freesurfer software based on subject 3 tesla MRI images. The normalized volume of cortical GM and cerebral WM were compared in two study groups, and then the asymmetry index (AI) of GM and WM atrophy was also assessed in two groups. Statistical analysis was constructed using a t-test with p < 0.05 of significance. Results No significant difference was observed in the volume of cortical GM and cerebral WM in the two study groups. The cortical GM asymmetry index in the PD-NC group was significantly (p = 0.01) higher than the HC group, however, no difference was observed for the cerebral WM asymmetry index. Conclusion Atrophy in cortical GM and WM was not observed between the PD-NC and the HC group, however, the asymmetry index in GM was significant between the two group. It seems that the brain’s bilateral balance has ruptured in PD. Cortical GM asymmetry in PD-NC can be considered a potent biomarker and should be investigated more in the future. In future studies, construction of a longitudinal study on this issue could be useful.