Alzheimer's disease (AD) as an advanced brain disorder may cause damage to the memory and tissue loss in the brain. Since AD is a mostly costly disease, various deep learning-based models have been presented to achieve a high accuracy classifier to Alzheimer's diagnosis. While a model with high discriminative features is required to obtain a high performance classifier, the lack of image samples in the datasets causes over-fitting and deteriorates the performance of deep learning models. To overcome this problem, few-shot learning such as deep metric learning was introduced. In this paper we employ a novel deep triplet network as a metric learning approach to brain MRI analysis and Alzheimer's detection. The proposed deep triplet network uses a conditional loss function to overcome the lack of limited samples and improve the accuracy of the model. The basic network of this model inspired by VGG16 and experiments are conducted on open access series of imaging studies (OASIS). The experiments show that the proposed model outperforms the state-of-the-art models in term of accuracy.