Devices in the Internet of things produce a lot of streaming data, such as environment perception data, industrial control, human health data, etc., all these data uploaded to the cloud server will cause a huge burden on network, and the cloud-edge collaborative calculation mode can greatly alleviate the pressure of the network bandwidth and the cloud computing, and expedite the processing of data, improve the service response ability. However, cloud-edge collaborative computing is also faced with problems such as data theft and tampering. Obviously, once these streaming data carrying important information are tampered with, it is likely to cause serious losses. Based on the chameleon authentication tree (CAT), this paper constructed a cloud-edge-device collaborative integrity verification model for streaming data (CCIVS-SD) that supports data confidentiality protection. The scheme includes five entities: devices, edge nodes, cloud servers, data users and trusted third parties, which can complete appending, query, and integrity verification of the streaming data, and can also protect data privacy.