Early Alzheimer's Disease (AD) or Mild Cognitive Impairment (MCI) can be diagnosed through proper examination of several brain biomarkers. In recent times, several high-dimensional classification techniques have been suggested to discriminate between AD and MCI on the basis of T1-weighted MRI of patients. These techniques have been implemented mostly from scratch, making it really difficult to achieve any meaningful result within a short span of time. Therefore, the classification of AD is usually a very daunting and time-consuming task. In our study, we trained high dimensional Deep Neural Network (DNN) models with transfer learning in order to achieve meaningful results very quickly in terms of detecting AD from fMRI image. The fMRI image dataset has been collected from Alzheimer's Disease Neuroimaging Initiative (ADNI). We have used three different DNN models for our study: VGG19, Inception v3, and ResNet50 to classify AD, MCI, and Cognitively Normal (CN) patients. Firstly, we implemented some pre-processing steps on the images and divided them into training, testing, and validation sets. Secondly, we initialized these DNN models with the weights from pre-existing models trained on the ImageNet dataset. Finally, we trained and evaluated all the DNN models. After a relatively short amount of training (15 epochs), we achieved an approximate of 90% accuracy with VGG19, 85% accuracy with Inception v3, and 70% with ResNet50. Thus, we achieved excellent classification accuracy in a very short time with our research. Contribution - Classification between early-stage and late- stage AD at improved accuracy with transfer learning.