Functional magnetic resonance imaging (fMRI) has been widely applied to analysis and diagnosis of brain diseases, including Alzheimer’s disease (AD) and its prodrome, i.e., mild cognitive impairment (MCI). Traditional methods usually construct connectivity networks (CNs) by simply calculating Pearson correlation coefficients (PCCs) between time series of brain regions, and then extract low-level network measures as features to train the learning model. However, the valuable observation information in network construction (e.g., specific contributions of different time points) and high-level (i.e., high-order) network properties are neglected in these methods. In this paper, we first define a novel weighted correlation kernel (called wc-kernel) to measure the correlation of brain regions, by which weighting factors are determined in a data-driven manner to characterize the contribution of each time point, thus conveying the richer interaction information of brain regions compared with the PCC method. Furthermore, we propose a wc-kernel based convolutional neural network (CNN) (called wck-CNN) framework for extracting the hierarchical (i.e., from low-order to high-order) functional connectivities for disease diagnosis, by using fMRI data. Specifically, we first define a layer to build dynamic CNs (DCNs) using the defined wc-kernels. Then, we define three layers to extract local (region specific), global (network specific) and temporal high-order properties from the constructed low-order functional connectivities as features for classification. Results on 174 subjects (a total of 563 scans) with rs-fMRI data from ADNI suggest that the our method can not only improve the performance compared with state-of-the-art methods, but also provide novel insights into the interaction patterns of brain activities and their changes in diseases.