The IoT devices are widely used in Industrial environment, but usually suffers the resource and energy bottlenecks which may affect the task processing efficiency. Computation offloading is a mechanism to utilize resources well by moving resource-intensive applications from terminal devices to network edge or cloud servers. However, there are still some challenges in applying computation offloading to the Industrial Internet environment due to the complexity and uncertainty of the actual industrial environment. Emerging Digital Twin (DT) is capable of predicting, estimating, and analyzing the real-time state of physical entities and monitoring system environments by creating virtual models of physical entities. Therefore, in this paper, we design a Digital Twin-assisted End-Edge-Cloud collaboration architecture for Industrial Internet (DT-EEC) and propose a computation offloading method based on Deep Reinforcement Learning (DRL) to minimize the average delay and energy consumption of task processing under this architecture. In addition, we find the extra delay and energy consumption caused by the unreliability of computing nodes are often ignored in previous studies, so the reliability of IoT terminal devices and edge servers are also considered in our computation offloading. The experimental results show the effectiveness of the proposed method in different scenarios.