Applying consortium blockchain as a trust layer for heterogeneous Industrial Internet-of-Things devices is cost-effective. However, with an increase in computing power, some powerful attacks (e.g. the 51% attack) are inevitable and will cause severe consequences. Recent studies also confirm that anonymity and immutability of blockchain have been abused to facilitate black market trades, etc. To operate controllable blockchain for IIoT devices, it is necessary to rewrite blockchain history back to a normal state once the chain is breached. Ateniese et al proposed redactable blockchain by using chameleon hash (CH) to replace traditional hash function, it allows blockchain history to be written when needed (EuroS and P 2017). However, we cannot apply this idea directly to IIoT without solving the following problems: (1) achieve a decentralized design of CH; (2) update the signatures accordingly to authenticate the redacted contents; (3) satisfy the low-computing need of the individual IIoT device. In this work, we overcome the above issues by proposing the first threshold chameleon hash (TCH) and accountable-and-sanitizable chameleon signature (ASCS) schemes. Based on them, we build a redactable consortium blockchain which is efficient for IIoT devices to operate. It allows a group of authorized sensors to write and rewrite blockchain without causing any hard forks. Basically, TCH is the first threshold chameleon hash and ASCS is a public-key signature supporting file-level and block-level modifications of signatures without impairing authentications. Additionally, ASCS achieves accountability to avoid abuse of redaction. While security analysis validates our proposals, the simulation results show that redaction is acceptably efficient if it is executed at a small scale or if we adopt a coarse-grained redaction while sacrificing some securities.