Neuroimaging data may reflect the mental status of both cognitively preserved individuals and patients with neurodegenerative diseases. To find the relationship between cognitive performance and the difference between predicted and observed functional test results, we developed a Convolutional Neural Network (CNN) based regression model to estimate the level of cognitive decline from preprocessed T1-weighted MRI images. In this study, we considered the Predicted Cognitive Gap (PCG) as the measure to accurately segregate Cognitively Normal (CN) versus Alzheimer disease (AD) subjects. The proposed model was tested on a dataset that includes 422 CN and 377 AD cases. The performance of the proposed solution was measured using Receiver Operating Characteristic (ROC) Area Under the Curve (AUC) and achieved 0.987 (ADAS-cog), 0.978 (MMSE), 0.898 (RAVLT), 0.848 (TMT), 0.829 (DSST) for averaged brain images; and 0.985 (ADAS-cog), 0.987 (MMSE), 0.901 (RAVLT), 0.8474 (TMT), 0.796 (DSST) for middle slice skull stripped brain images. The results achieved indicate that PCG can accurately separate healthy subjects from demented ones. The structure of the brain contributes to the level of human cognition and their functional abilities. Proposed PCG may aid in diagnostics of dementia.