Individualized human cerebral cartography has drawn considerable attention in neuroscience research. But many challenges remain, mainly due to large cross-subject variations in brain morphology, connectivity, and function. We developed a new tool called brain atlas individualization network (BAI-Net) that automatically parcels individual cerebral cortex into segregated functional areas using structural and diffusion MRIs. The presented method integrates the group priors into the loss function of graph convolution network, and learns the connectivity context of anatomical fingerprints for each area on individual brain graphs. The presented model provides reliable, efficient and explainable individual cortical parcellations across multiple sessions with different scanners. Moreover, it keeps highly group consistence as well as individual-specific variations. Given the reliable inter-subject variabilities from BAI-Net parcellation, their functional connectome showed higher associations with individual behavioral scores in a cognitive battery, compared to the individualized methods. The presented model has potential applications in locating more individual-specific regions in the diagnosis and treatment of neurological disorders, rather than group-registered method in terms of cortical morphology. And its methodology could be applied to individualize many population brain atlases.