Alzheimer's disease (AD) is a neurodegenerative disease that causes memory loss and is considered the most common type of dementia. In many countries, AD is commonly affecting senior citizens having an aged more than 65 years. Machine learning-based approaches have some limitations due to data pre-processing issues. We propose a health care intelligent system based on a deep convolutional neural network (DCNN) in this research work. It classifies normal control (NC), mild cognitive impairment (MCI), and AD. The proposed model is employed on white matter (WM), and grey matter (GM) tissues with more cognitive decline features. In the experimental process, we used 375 Magnetic Resonance Image (MRI) subjects collected from Alzheimer's disease neuroimaging initiative (ADNI), including 130 NC people, 120 MCI patients, and 125 AD patients. We extract three major regions during pre-processing, that is, WM, GM and cerebrospinal fluid (CSF). This study shows promising classification results for NC versus AD 97.94%, MCI versus AD 92.84%, and NC versus MCI 88.15% on GM images. Furthermore, our proposed model attained 95.97%, 90.82%, and 86.87% on the same three binary classes on WM tissue, respectively. When comparing existing studies in terms of accuracy and other evaluation parameters, we found that our proposed approach shows better results than those approaches based on the CNN method.