Blockchain is a technology that can ensure data integrity in a distributed network, and it is actively applied in various fields. Recently, blockchain is gaining attention due to combining with the Internet of Things (IoT) technology in the industrial field. Moreover, many researchers have proposed the Industrial IoT (IIoT) architecture with blockchain for data integrity and efficient management. The IIoT network consists of many heterogeneous devices (e.g., sensors, actuators, and programmable logic controllers (PLC)) with resources-constrained, and the availability of the network must be preferentially considered. Therefore, applying the existed blockchain technology is still challenging. There are some results about the technique of constructing blockchain lightly to solve this challenge. However, in these results, the analysis in perspective of cryptographic performance (area, throughput, and power consumption) has not been considered sufficiently, or only focused on the architecture of the blockchain network. The blockchain technology is based on cryptographic techniques, and the main part is a cryptographic hash function. Therefore, if we construct the blockchain-based IIoT architecture, we have to consider the performance of the hash function. Many lightweight hash functions have been proposed recently for the resource-constrained environment, and it can also be used to the blockchain. Therefore, in this paper, we analyze the considerations of lightweight blockchain for IIoT. Also, we conduct an analysis of lightweight hash for blockchain, and propose a new lightweight hash-based blockchain architecture that can change the hash algorithm used for mining adjust to network traffic.