Effective fusion of multi-modality neuroimaging data, such as structural magnetic resonance imaging (MRI) and fluorodeoxyglucose positron emission tomography (PET), has attracted increasing interest in computer-aided brain disease diagnosis, by providing complementary structural and functional information of the brain to improve diagnostic performance. Although considerable progress has been made, there remain several significant challenges in traditional methods for fusing multi-modality data. First, the fusion of multi-modality data is usually independent of the training of diagnostic models, leading to sub-optimal performance. Second, it is challenging to effectively exploit the complementary information among multiple modalities based on low-level imaging features (e.g., image intensity or tissue volume). To this end, in this paper, we propose a novel Deep Latent Multi-modality Dementia Diagnosis (DLMD2) framework based on a deep non-negative matrix factorization (NMF) model. Specifically, we integrate the feature fusion/learning process into the classifier construction step for eliminating the gap between neuroimaging features and disease labels. To exploit the correlations among multi-modality data, we learn latent representations for multi-modality data by sharing the common high-level representations in the last layer of each modality in the deep NMF model. Extensive experimental results on the Alzheimer’s Disease Neuroimaging Initiative (ADNI) dataset validate that our proposed method outperforms several state-of-the-art methods.