Alzheimer’s disease (AD) is a complex neuro-degenerative disorder that profoundly affects the cognitive ability of millions of people worldwide. Because there is no cure for AD, it is substantially important to detect the disease in its early stage to mitigate its effects. This study has designed a classifier system that classify Alzheimer’s Magnetic Resonance Imaging (MRI) images into four classes: Very Mild Demented (AD), early mild demented (EMCI), late mild demented (LMCI) and Non Demented (NC). The system has been designed by means of fully-connected Convolutional Neural Network (CNN) architecture as well as ResNet50, VGG and EfficientNet B0 architectures. The input is taken from Kaggle Alzheimer’s Dataset, which consists of a total of 6400 images. The best system performance has been carried out with RMSProp optimizer, resulting in the highest test accuracy value of 84% using VGG architectures. Additionally, as the image sizes increase, the VGG accuracy improves. Based on the performance results, the system shows that the CNN model with VGG architecture is better suited for classifying Alzheimer’s disease.