Billions of Internet of Thing (IoT) devices are deployed in edge network. They are used to monitor specific event, process and to collect huge data to control center with smart decision based on the collected data. However, some malicious IoT devices may interrupt and interfere with normal nodes in data collection, causing damage to edge network. Due to the open character of the edge network, how to identify the credibility of these nodes, thereby identifying malicious IoT devices, and ensure reliable data collection in the edge network is a great challenge. In this paper, an Active and Verifiable Trust Evaluation (AVTE) approach is proposed to identify the credibility of IoT devices, so to ensure reliable data collection for Edge Computing with low cost. The main innovations of the AVTE approach compared with the existing work are as follows: (1) In AVTE approach, the trust of the device is obtained by an actively initiated trusted detection routing method. It is fast, accurate and targeted. (2) The acquisition of trust in the AVTE approach is based on a verifiable method and it ensures that the trust degree has higher reliability. (3) The trust acquisition method proposed in this paper is low-cost. An encoding returned verification method is applied to obtain verification messages at a very low cost. This paper proposes an encoding returned verification method, which can obtain verification messages at a very low cost. In addition, the strategy of this paper adopts initiation and verification of adaptive active trust detection according to the different energy consumption of IoT devices, so as to reliably obtain the trust of device under the premise of ensuring network lifetime. Theoretical analysis shows that AVTE approach can improve the data collection rate by 0.5 ~ 23.16% while ensuring long network lifetime compared with the existing scheme.