The human brain can be inherently modeled as a brain network, where nodes denote billions of neurons and edges denote massive connections between neurons. Analysis on functional brain networks provides powerful abilities to discover potential mechanisms of human brain, and to aid brain disease detection, such as AD (Alzheimer’s disease). Effective discrimination of patients of AD and MCI (mild cognitive impairment) from NC (normal control) is important for the early diagnosis of AD. Therefore, this paper explores the problem of brain network classification for AD detection. Two deep learning methods of functional brain network classification are designed. The convolutional learning method learns the deep regional-connectivity features, while the recurrent learning method learns the deep adjacent positional features. The ELM (extreme learning machine)-boosted structure is also implemented to further improve the learning ability. Extensive experiments are conducted to evaluate and compare the AUC (area under curve), accuracy, recall, and training time of the proposed methods on a real-world dataset. Results indicate that (1) the proposed methods which learn deep features directly from brain networks outperform shallow learning methods and (2) models with the ELM-boosted structure achieve a higher performance. This paper explores the brain networks learning with deep features and ELM. The results demonstrate that the proposed methods provide a satisfactory learning ability in the application of AD detection.