Dementia, Alzheimer's disease (AD) in particular is a global problem and big threat to the aging population. An image based computer-aided dementia diagnosis method is needed to providing doctors help during medical image examination. Many machine learning based dementia classification methods using medical imaging have been proposed and most of them achieve accurate results. However, most of these methods make use of supervised learning requiring fully labeled image dataset, which usually is not practical in real clinical environment. Using large amount of unlabeled images can improve the dementia classification performance. In this study we propose a new semi-supervised dementia classification method based on random manifold learning with affinity regularization. Three groups of spatial features are extracted from positron emission tomography (PET) images to construct an unsupervised random forest which is then used to regularize the manifold learning objective function. The proposed method, stat-of-the-art Laplacian support vector machine (LapSVM) and supervised SVM are applied to classify AD and normal controls (NC). The experiment results show that learning with unlabeled images indeed improves the classification performance. And our method outperforms LapSVM on the same dataset.