Attention-deficit/hyperactivity disorder (ADHD) is a common neurodevelopmental disorder. Adults with ADHD continue to exhibit deficits in attention and executive function, whereas the neural mechanisms underlying visual mismatch negativity (vMMN)-related processing remain unclear. This study investigated the functional brain connectivity characteristics of adults with ADHD by combining standardized low-resolution brain electromagnetic tomography (sLORETA), phase-locking value (PLV) analysis, and a graph convolutional network (GCN) based on a visual Oddball paradigm that elicited vMMN responses. Electroencephalography (EEG) data were collected from 10 adults with ADHD and 10 healthy controls using a 128-channel recording system. Source signals from 68 brain regions defined by the Desikan-Killiany atlas were reconstructed using sLORETA. Functional connectivity networks were constructed using PLV and subsequently classified by the GCN model. The results showed that the accuracy, precision, recall, and F1-score of the GCN model under five-fold cross-validation were (85.13 ± 1.94)%, (80.58 ± 2.08)%, (86.04 ± 1.76)%, and (83.21 ± 1.89)%, respectively. Node feature weights and classification contribution analyses identified the lingual gyrus, calcarine fissure and surrounding cortex, parahippocampal gyrus, and precuneus as highly discriminative brain regions. These findings indicate that adults with ADHD exhibit abnormal functional connectivity patterns during vMMN-related processing and provide evidence for the auxiliary identification and neural mechanism investigation of ADHD.