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Advances in deep neural networks (DNN) greatly bolster real-time detection of anomalous IoT data. However, IoT devices can barely afford complex DNN models due to limited computational power and energy supply. While one can offload anomaly detection tasks to the cloud, it incurs long delay and requires large bandwidth when thousands of IoT devices stream data to the cloud concurrently. In this paper, we propose an adaptive anomaly detection approach for hierarchical edge computing (HEC) systems to solve this problem. Specifically, we first construct three anomaly detection DNN models of increasing complexity, and associate them with the three layers of HEC from bottom to top, i.e., IoT devices, edge servers, and cloud. Then, we design an adaptive scheme to select one of the models based on the contextual information extracted from input data, to perform anomaly detection. The selection is formulated as a contextual bandit problem and is characterized by a single-step Markov decision process, with an objective of achieving high detection accuracy and low detection delay simultaneously. We evaluate our proposed approach using a real IoT dataset, and demonstrate that it reduces detection delay by 84% while maintaining almost the same accuracy as compared to offloading detection tasks to the cloud. In addition, our evaluation also shows that it outperforms other baseline schemes.