Alzheimer’s disease (AD) constitutes a neurodegenerative pathology that presents mobility disorders as one of its earliest symptoms. Current smartphones integrate accelerometers that can be used to collect mobility data of Alzheimer’s patients. This paper describes a method that processes these accelerometer data and a convolutional neural network (CNN) that classifies the stage of the disease according to the mobility patterns of the patient. The method is applied in a case study with 35 Alzheimer’s patients, in which a classification success rate of 91% was obtained.