For reliable large-scale quantum computation, quantum error correction (QEC) is essential to protect logical information distributed across multiple physical qubits. Taking advantage of recent advances in deep learning, neural network-based decoders have emerged as a promising approach to improve the reliability of QEC. We propose the qubit-centric transformer (QCT), a novel QEC decoder for stabilizer codes based on a transformer architecture with a qubit-centric attention mechanism. Our decoder transforms input syndromes from the stabilizer domain into qubit-centric tokens via a specialized embedding strategy. These qubit-centric tokens are processed through attention layers to effectively identify the underlying logical error. Furthermore, we introduce a graph-based masking method that incorporates the topological structure of quantum codes, enforcing attention toward relevant qubit interactions. Across various code distances for surface codes, QCT achieves strong decoding performance, significantly outperforming existing neural decoders and the belief propagation (BP) with ordered statistics decoding (OSD) baseline. Notably, QCT achieves a high threshold of 18.1% under the code-capacity noise model, which closely approaches the theoretical bound of 18.9% and surpasses both the BP+OSD and the minimum-weight perfect matching (MWPM) thresholds, while also exhibiting a substantially higher error suppression factor. Furthermore, we extend QCT to the circuit-level noise model by incorporating temporal convolution blocks to process repeated syndrome measurements. Under realistic circuit-level noise conditions, QCT demonstrates scalable error suppression across the evaluated code distances, consistently outperforming advanced decoders including the correlated MWPM and BP+OSD. This qubit-centric approach provides a scalable and robust framework for surface code decoding, advancing the path toward fault-tolerant quantum computing.