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Internet of things is characterized by limited energy and distributed topology. In this scenario, a secure and energy-saving routing algorithm plays a significant role in ensuring the performance of Internet of things. Due to different standards and communication stacks, traditional security mechanisms heavily rely on trust management to function well. In this article, we propose an energy-aware trustworthy multi-hop routing model for Internet of things. To balance energy consumption and trust, the whole routing from source to destination should be considered for trust appraisal, rather than the destination peers merely. Meanwhile, the energy consumption of wise interaction should be regarded as one criterion. We also introduce a trustworthy spanning tree algorithm that is able to balance energy consumption and reduce trust cost. The experimental results suggest that the proposed strategy can lower energy consumption significantly under the premise of trustworthy transmission.