The verifiable data streaming (VDS) protocol enables clients to delegate locally generated data items (i.e., data streaming) to a semi-honest cloud server in real time while maintaining data integrity. It is built upon a chameleon authentication tree (CAT) and digital signatures. That is, a user may confirm the retrieved data item’s integrity by recomputing the hash value on its underlying CAT root and further checking a signature of this value created by the data owner. However, many lightweight application scenarios may not deploy public-key infrastructure (PKI) to support the digital signatures. Moreover, in frequently updated application scenarios such as trend analysis and stock forecasting, many new digital signatures are generated, and malicious cloud servers might return old versions of a queried outsourced data item and the corresponding signature. Consequently, maintaining those previously created signatures becomes a challenge. In this paper, to overcome these issues, we put forth a novel construction framework of VDS by introducing a redactable blockchain. Specifically, we treat the root value of the CAT as a transaction and package it to a redactable blockchain. After that, the immutability of the underlying redactable blockchain ensures the integrity of outsourced data streaming and avoids using the digital signature. Also, as the data is updated, we can update the root value of the CAT by re-editing the corresponding block. We also put a concrete VDS construction in the new framework, and formally prove its security. Theoretical compression and experimental results indicate that the proposed VDS protocol has merits in functionality and practicality.