Triggered by the success of transformers in various visual tasks, the spatial self-attention mechanism has recently attracted more and more attention in the computer vision community. However, we empirically found that a typical vision transformer with the spatial self-attention mechanism could not learn accurate attention maps for distinguishing different categories of fine-grained images. To address this problem, motivated by the temporal attention mechanism in brains, we propose a hierarchical attention network for learning fine-grained feature representations, called HAN, where the features learnt by implementing a sequence of spatial self-attention operations corresponding to multiple moments are aggregated progressively. The proposed HAN consists of four modules: a self-attention backbone module for learning a sequence of features with selfattention operations, a spatial feature self-organizing module for facilitating the model training, a hierarchical aggregation module for aggregating the re-organized features via a Long Short-Term Memory network, and a context-aware module that is implemented as the forget block of the hierarchical aggregation module for preserving/forgetting the long-term memory by utilizing contextual information. Then, we propose a HAN-based method for open-set fine-grained recognition by integrating the proposed HAN network with a linear classifier, called HAN-OSFGR. Extensive experimental results on 3 fine-grained datasets and 2 coarse-grained datasets demonstrate that the proposed HAN-OSFGR outperforms 9 state-of-the-art open-set recognition methods significantly in most cases.