The Internet of Things plays an important role in the process of industrial intelligence. It facilitates the connection between devices and the Internet to enable the gathering and analysis of industrial data. However, industrial Internet of Things (IIoT) applications are highly susceptible to latency, have strict energy consumption limitations, and impose specific demands on the resources of IIoT devices. Fortunately, edge computing can migrate tasks to the edge server or cloud platform to deal with the above shortcomings. Nevertheless, tasks generated by IIoT devices in industrial production have a higher rate of repetition, and repetitive execution of the same task diminishes the operational efficiency of the edge system. In this regard, we can cache high-value tasks through task caching to reduce redundant execution. The aforementioned idea can be described as a joint optimization problem of computation offloading and task caching with resource constraints in IIoT. To address this challenge, we establish an edge-empowered service model and propose a cache-assisted computation offloading algorithm for IIoT applications. Extensive experiments demonstrate that the proposed algorithm outperforms some critical methods in terms of energy consumption and latency.