The Industrial Internet of Things (IIoT) is increasingly utilized in the industrial sector to enhance production efficiency, improve product quality, and reduce costs. Due to its decentralized nature, tamper-resistance, and traceability, consortium blockchain has extensive applications in IIoT. Byzantine Fault Tolerance (BFT) consensus protocols are widely used in consortium blockchain systems. However, typical BFT consensus protocols cannot detect and remove faulty nodes, thereby introducing security and performance issues, which are particularly severe for IIoT due to its weak security and limited resources. To address these issues, we present Fault-Removable Byzantine Fault Tolerance (FRBFT) protocol, a synchronous BFT consensus protocol that can detect and remove faulty nodes. If a faulty node keeps silent or equivocates, it could be detected and removed by all the honest nodes from the system in the next iteration. Our evaluations show that FRBFT can detect and remove 8 faulty nodes out of 17 nodes within 1.4 s, with a throughput of 19.8 Kops/sec and a latency of 118.7 ms, which has better security and performance than Sync Hotstuff and is more suitable for application in IIoT scenarios.