<p>With the booming of industrial internet, the demand for computing resources is increasing. The traditional cloud computing cannot adapt to the current industrial requirements for low delay of computing resources and privacy protecting during data storage and transmission. To address these challenges, edge computing (EC) has emerged as a new paradigm, enhancing task processing and response speed while mitigating data leakage risks through decentralized processing at the edge. Since the task offloading directly affects the operation efficiency of the EC system. Unreasonable task offloading will not improve or even reduce the EC performance. However, industrial internet imposes high demands on delay and privacy. To address the task offloading issue facing industrial internet, this paper first establishes a joint task caching and privacy protecting EC task offloading model, which aims to reduce the delay while ensuring the data privacy. Secondly, to solve the offloading strategy from the established model, a task offloading algorithm based on the improved pathfinder algorithm and simulated annealing algorithm is proposed. The proposed offloading algorithm searches for the optimal solution through the improved pathfinder algorithm, in which we add a mechanism of replenishing the number of individuals in the population and a mechanism of updating individuals with low fitness to speed up the convergence of finding the near-optimal solution. Moreover, the simulated annealing algorithm is used to prevent premature convergence. Finally, the established task offloading model improves the objective value by 49.93% over the local computation, which is important for protecting data privacy and improving response speed. Simulation results show that compared with the existing offloading algorithms, the proposed algorithm is at least 1.53% faster than others, with faster optimal solution-solving capability.</p>