We investigated whether pre-operative MRI measures of focal brain atrophy could predict cognitive decline occurring after deep brain stimulation (DBS) of the subthalamic nucleus (STN) in patients with Parkinson’s disease (PD). For that purpose, we prospectively collected data of 42 consecutive patients with PD who underwent bilateral STN-DBS. Normalized brain structure volumes and cortical thicknesses were measured on pre-operative T1-weighted MRI. Patients were tested for their cognitive performances before surgery and 1 year after. After controlling for age, gender, pre-operative disease severity, change in dopaminomimetic dose after surgery and contact location, we found correlations: (1) between the variation of the total Mattis dementia rating scale (MDRS) score and left lateral ventricle volume (p = 0.032), (2) between the variation of the initiation/perseveration subscore of the MDRS and the left nucleus accumbens volume (p = 0.042) and the left lateral ventricle volume (p = 0.017) and (3) between the variation of the backward digit-span task and the right and left superior frontal gyrus thickness (p = 0.004 and p = 0.007, respectively). Left nucleus accumbens atrophy was associated with decline in the initiation/perseveration subscore with the largest effect size (d = − 1.64). Pre-operative left nucleus accumbens volume strongly predicted postoperative decline in the initiation/attention subscore (AUC = 0.92, p < 0.001, 96.3% sensitivity, 80.0% specificity, 92.9% PPV and 92.9% NPV). We conclude that the morphometric measures of brain atrophy usually associated with cognitive impairment in PD can also explain or predict a part of cognitive decline after bilateral STN-DBS. In particular, the left accumbens nucleus volume could be considered as a promising marker for guiding surgical decisions.