With the rapid development of industrial internet of thing (IIoT), the distributed topology of IIoT and resource constraints of edge computing conduct new challenges to traditional data storage, transmission, and security protection. A distributed trust and allocated ledger of blockchain technology are suitable for the distributed IIoT, which also becomes an effective method for edge computing applications. This paper proposes a resource constrained Layered Lightweight Blockchain Framework (LLBF) and implementation mechanism. The framework consists of a resource constrained layer (RCL) and a resource extended layer (REL) blockchain used in IIoT. We redesign the block structure and size to suit to IIoT edge computing devices. A lightweight consensus algorithm and a dynamic trust right algorithm is developed to improve the throughput of blockchain and reduce the number of transactions validated in new blocks respectively. Through a high throughput management to guarantee the transaction load balance of blockchain. Finally, we conducted kinds of blockchain simulation and performance experiments, the outcome indicated that the method have a good performance in IIoT edge application.