Deploying task caching at edge servers has become an effective way to handle compute-intensive and latency-sensitive tasks on the industrial internet. However, how to select the task scheduling location to reduce task delay and cost while ensuring the data security and reliable communication of edge computing remains a challenge. To solve this problem, this paper establishes a task scheduling model with joint blockchain and task caching in the industrial internet and designs a novel blockchain-assisted caching mechanism to enhance system security. In this paper, the task scheduling problem, which couples the task scheduling decision, task caching decision, and blockchain reward, is formulated as the minimum weighted cost problem under delay constraints. This is a mixed integer nonlinear problem, which is proved to be nonconvex and NP-hard. To solve the optimal solution, this paper proposes a task scheduling strategy algorithm based on an improved genetic algorithm (IGA-TSPA) by improving the genetic algorithm initialization and mutation operations to reduce the size of the initial solution space and enhance the optimal solution convergence speed. In addition, an Improved Least Frequently Used algorithm is proposed to improve the content hit rate. Simulation results show that IGA-TSPA has a faster optimal solution-solving ability and shorter running time compared with the existing edge computing scheduling algorithms. The established task scheduling model not only saves 62.19% of system overhead consumption in comparison with local computing but also has great significance in protecting data security, reducing task processing delay, and reducing system cost.