Function connectivity networks (FCNs) based on resting-state functional magnetic resonance imaging (rs-fMRI) have been used for analysis of brain diseases, such as Alzheimer’s disease (AD) and Attention Deficit Hyperactivity Disorder (ADHD). However, existing studies usually extract meaningful measures (e.g., local clustering coefficients) from FCNs as a feature vector for brain disease classification, and perform vector-based feature selection methods (e.g., t-test) to improve the performance of learning model, thus ignoring important structural information of FCNs. To address this problem, we propose a graph-kernel-based structured feature selection (gk-MTSFS) method for brain disease classification using rs-fMRI data. Different with existing method that focus on vector-based feature selection, our proposed gk-MTSFS method adopts the graph kernel (i.e., kernel constructed on graphs) to preserve the structural information of FCNs, and uses the multi-task learning to explore the complementary information of multi-level thresholded FCNs (i.e., thresholded FCNs with different thresholds). Specifically, in the proposed gk-MTSFS model, we first develop a novel graph-kernel based Laplacian regularizer to preserve the structural information of FCNs. Then, we employ an 2,1-norm based group sparsity regularizer to joint select a small amount of discriminative features from multi-level FCNs for brain disease classification. Experimental results on both ADNI and ADHD-200 datasets with rs-fMRI data demonstrate the effectiveness of our proposed gk-MTSFS method in rs-fMRI-based brain disease diagnosis.