Nowadays, driven by the rapid development of smart mobile equipments and 5G network technologies, the application scenarios of Internet of Things (IoT) technology are becoming increasingly widespread. The integration of IoT and industrial manufacturing systems forms the industrial IoT (IIoT). Because of the limitation of resources, such as the computation unit and battery capacity in the IIoT equipments (IIEs), computation-intensive tasks need to be executed in the mobile edge computing (MEC) server. However, the dynamics and continuity of task generation lead to a severe challenge to the management of limited resources in IIoT. In this article, we investigate the dynamic resource management problem of joint power control and computing resource allocation for MEC in IIoT. In order to minimize the long-term average delay of the tasks, the original problem is transformed into a Markov decision process (MDP). Considering the dynamics and continuity of task generation, we propose a deep reinforcement learning-based dynamic resource management (DDRM) algorithm to solve the formulated MDP problem. Our DDRM algorithm exploits the deep deterministic policy gradient and can deal with the high-dimensional continuity of the action and state spaces. Extensive simulation results demonstrate that the DDRM can reduce the long-term average delay of the tasks effectively.