Task offloading and resource allocation are fundamental and crucial for the edge computing-enhanced industrial Internet of things, where the security and credibility among massive heterogeneous devices are being challenged. This paper first proposes a novel blockchain consensus scheme named replicated and Byzantine fault tolerant, which can enhance the trust among nodes with the low communication cost. Then, with the objective of minimizing the task completion time, which includes credible verification, task offloading and transaction record, a joint task offloading and resource allocation problem with respect to blockchain verification ratio, offloading decision, communication and computing resources is formulated. Due to its non-convexity and the decentralized characteristic of blockchain, a multi-agent deep reinforcement learning algorithm with deterministic policy gradient is proposed to appropriate the optimal solution. Experiment results confirm the effectiveness of the proposed scheme in guaranteeing the timeliness and security.