Learning discriminative and rich features is an important research task for person re-identification. Previous studies have attempted to capture global and local features at the same time and layer of the model in a non-interactive manner, which are called synchronous learning. However, synchronous learning leads to high similarity, and further defects in model performance. To this end, we propose asynchronous learning based on the human visual perception mechanism. Asynchronous learning emphasizes the time asynchrony and space asynchrony of feature learning and achieves mutual promotion and cyclical interaction for feature learning. Furthermore, we design a dynamic progressive refinement module to improve local features with the guidance of global features. The dynamic property allows this module to adaptively adjust the network parameters according to the input image, in both the training and testing stage. The progressive property narrows the semantic gap between the global and local features, which is due to the guidance of global features. Finally, we have conducted several experiments on four datasets, including Market1501, CUHK03, DukeMTMC-ReID, and MSMT17. The experimental results show that asynchronous learning can effectively improve feature discrimination and achieve strong performance.