Prediction of the cognitive evolution of a person susceptible to develop a neurodegenerative disorder is crucial to provide an appropriate treatment as soon as possible. In this paper we propose a 3D siamese network designed to extract features from whole-brain 3D MRI images. We show that it is possible to extract meaningful features using convolution layers, reducing the need of classical image processing operations such as segmentation or pre-computing features such as cortical thickness. To lead this study we used the Alzheimer's Disease Neuroimaging Initiative (ADNI), a public data base of 3D MRI brain images. A set of 247 subjects has been extracted, all of the subjects having 2 images in a range of 12 months. In order to measure the evolution of the patients states we have compared these 2 images. Our work has been inspired at the beginning by an article of Bhagwat et al. in 2018, who have proposed a siamese network to predict the status of patients but without any convolutional layers and reducing the MRI images to a vector of features extracted from predefined ROIs. We show that our network achieves an accuracy of 90\% in the classification of cognitively declining VS stable patients. This result has been obtained without the help of a cognitive score and with a small number of patients comparing to the current datasets size claimed in deep learning domain.