Attention-Deficit/Hyperactivity Disorder (ADHD) is one of the most common childhood neuropsychiatric disorders, with characteristic symptoms of age-inappropriate levels of inattention, hyperactivity, and impulsivity that interfere with social and academic functioning. Recent studies have demonstrated that beyond purely neuroanatomical alterations, the disorder implies altered functional connectivity in several large-scale brain functional networks. In this study, we use the Graph Convolutional Networks (GCNs), which represent the population of patients and control subjects as a sparse graph. In this sparse graph, nodes are human subjects, which are associated with a brain connectivity-based feature vector, and edges are weighted using phenotypic information. We applied this framework on the large publicly available multi-institution ADHD-200 data repository of 921 resting-state functional MRI data sets. Using a 10k-fold cross-validation procedure, we obtain a mean accuracy of 76.95 and mean Area Under the receiver operating Curve (AUC) of 79.66 between typical controls and the ADHD Combined subtype. In addition, we performed classification between typical controls and all subtypes of ADHD patients, where we obtained a mean accuracy of 69.53 and mean AUC of 74.76, which outperforms the state-of-the-art methods in the literature. Our results suggest that resting-state functional MRI analysis with GCNs may provide contributions to developing biomarkers in ADHD and other neurological disorders.