Current atlas-based approaches to brain network analysis rely heavily on standardized anatomical or connectivity-driven brain atlases. However, these fixed atlases often introduce significant limitations, such as spatial misalignment across individuals, functional heterogeneity within predefined regions, and atlas-selection biases, collectively undermining the reliability and interpretability of the derived brain networks. To address these challenges, we propose a novel atlas-free brain network transformer (atlas-free BNT) that leverages individualized brain parcellations derived directly from subject-specific resting-state fMRI data. Our approach computes ROI-to-voxel connectivity features in a standardized voxel-based feature space, which are subsequently processed using the BNT architecture to produce comparable subject-level embeddings. Experimental evaluations on sex classification and brain-connectome age prediction tasks demonstrate that our atlas-free BNT consistently outperforms state-of-the-art atlas-based methods, including elastic net, BrainGNN, Graphormer and the original BNT. Our atlas-free approach significantly improves the precision, robustness, and generalizability of brain network analyses. This advancement holds great potential to enhance neuroimaging biomarkers and clinical diagnostic tools for personalized precision medicine. Reproducible code is available at https://github.com/shuai-huang/atlas_free_bnt