Brain parcellation helps to understand the structural and functional organization of the cerebral cortex. Resting-state functional magnetic resonance imaging (fMRI) and connectivity analysis provide useful information to delineate individual brain parcels in vivo. We proposed an individualized cortical parcellation based on graph neural networks (GNN) to learn the reliable functional characteristics of each brain parcel on a large fMRI dataset and to infer the areal probability of each vertex on unseen subjects. A subject-specific confidence mask was implemented in the GNN model to account for the tradeoff between the topographic alignment across subjects and functional homogeneity of brain parcels on individual brains. The individualized brain parcellation achieved better functional homogeneity at rest and during cognitive tasks compared with the group-registered atlas (p-values < 0.05). In addition, highly reliable and replicable parcellation maps were generated on multiple sessions of the same subject (intrasubject similarity = 0.89), while notable variations in the topographic organization were captured across subjects (intersubject similarity = 0.81). Moreover, the intersubject variability of brain parcellation indicated large variations in the association cortices while keeping a stable parcellation on the primary cortex. Such topographic variability was strongly associated with the functional connectivity variability, significantly predicted cognitive behaviors, and generally followed the myelination, cytoarchitecture, and functional organization of the human brain. This study provides new avenues to the precise individualized mapping of the cortical areas through deep learning and shows high potentials in the personalized localization diagnosis and treatment of neurological disorders.