Machine learning techniques have been widely used to detect morphological abnormalities from structural brain magnetic resonance imaging data and to support the diagnosis of neurological diseases such as dementia. In this paper, we propose to use a multiple instance learning (MIL) method in an application for the detection of Alzheimer’s disease (AD) and its prodromal stage mild cognitive impairment (MCI). In our work, local intensity patches are extracted as features. However, not all the patches extracted from patients with dementia are equally affected by the disease and some of them may not be characteristic of morphology associated with the disease. Therefore, there is some ambiguity in assigning disease labels to these patches. The problem of the ambiguous training labels can be addressed by weakly supervised learning techniques such as MIL. A graph is built for each image to exploit the relationships among the patches and then to solve the MIL problem. The constructed graphs contain information about the appearances of patches and the relationships among them, which can reflect the inherent structures of images and aids the classification. Using the baseline MR images of 834 subjects from the ADNI study, the proposed method can achieve a classification accuracy of 89% between AD patients and healthy controls, and 70% between patients defined as stable MCI and progressive MCI in a leave-one-out cross validation. Compared with two state-of-the-art methods using the same dataset, the proposed method can achieve similar or improved results, providing an alternative framework for the detection and prediction of neurodegenerative diseases.