Brain connectivity network has been used for diagnosis and classification of neurodegenerative diseases, such as Alzheimer's disease (AD) as well as its early stage, i.e., mild cognitive impairment (MCI). However, conventional connectivity network is usually constructed based on the pairwise correlation among brain regions and thus ignores the higher-order relationship among them. Such information loss is unexpected because the brain itself is a complex network and the higher-order interaction may contain useful information for classification. Accordingly, in this paper, we propose a new brain connectivity hyper-network based method for MCI classification. Here, the connectivity hyper-network denotes a network where an edge can connect more than two brain regions, which can be naturally represented with a hyper-graph. Specifically, we first construct connectivity hyper-networks from the resting-state fMRI time series using sparse representation modeling. Then, we extract three sets of the brain-region specific features from the connectivity hyper-networks, and exploit a manifold regularized multi-task feature selection method to jointly select the most discriminative features. Finally, we use multi-kernel support vector machine (SVM) for classification. The experimental results demonstrate the efficacy of our proposed method for MCI classification with comparison to the conventional connectivity network based methods.