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The brain age has been proven to be a phenotype of relevance to cognitive performance and brain disease. Achieving accurate brain age prediction is an essential prerequisite for optimizing the predicted brain-age difference as a biomarker. As a comprehensive biological characteristic, the brain age is hard to be exploited accurately with models using feature engineering and local processing such as local convolution and recurrent operations that process one local neighborhood at a time. Instead, Vision Transformers learn global attentive interaction of patch tokens, introducing less inductive bias and modeling long-range dependencies. In terms of this, we proposed a novel network for learning brain age interpreting with global and local dependencies, where the corresponding representations are captured by Successive Permuted Transformer (SPT) and convolution blocks. The SPT brings computation efficiency and locates the 3D spatial information indirectly via continuously encoding 2D slices from different views. Finally, we collect a large cohort of 22645 subjects with ages ranging from 14 to 97 and our network performed the best among a series of deep learning methods, yielding a mean absolute error (MAE) of 2.855 in validation set, and 2.911 in an independent test set.