Federated learning, as a compelling machine learning framework, enables collaborative model training without exposing private data. However, the excessive communication overhead remains a major challenge. To tackle this challenge, hierarchical federated edge learning (HFEL) framework has been proposed for reducing the communication load via migrating the model aggregation partially from cloud to edge servers. Although HFEL has significant potential, it is still constrained by end-devices with limited computational capabilities and unfavorable network conditions. A common approach to reduce this effect is to involve only the fastest end-devices in the training process. But because only parts of end-devices' data samples can be selected by such means, it damages the diversity of training data, and hence greatly affects the model's quality. In addition, for further improving the training performance, a proper bandwidth allocation strategy is also needed to make full use of the shared network resource of edge servers. To this end, we proposeDAHFF, aDiversity-AwareHierarchicalFastFederated learning framework consisting ofVirtual Queue based Device Selectionphase andBinary Search based Bandwidth Allocation, which are responsible for selecting participated end-devices and allocating bandwidth for selected devices, respectively. Extensive experiments on different deep learning models show that our proposed framework can averagely speed up the training performance by$2.07\times$in comparison with state-of-the-art approaches.