Fog computing system is able to facilitate computation-intensive applications and emerges as one of the promising technology for realizing the Internet of Things (IoT). By offloading the computational tasks to the fog node (FN) at the network edge, both the service latency and energy consumption can be improved, which is significant for industrial IoT applications. However, the dynamics of computational resource usages in the FN, the radio environment and the energy in the battery of IoT devices make the offloading mechanism design become challenging. Therefore, in this article, we propose a dynamic optimization scheme for the IoT fog computing system with multiple mobile devices (MDs), where the radio and computational resources, and offloading decisions, can be dynamically coordinated and allocated with the variation of radio resources and computation demands. Specifically, with the objective to minimize the system cost related to latency, energy consumption, and weights of MDs, we propose a joint computation offloading and radio resource allocation algorithm based on Lyapunov optimization. Through minimizing the derived upper bound of the Lyapunov drift-plus-penalty function, we divide the main problem into several subproblems at each time slot and address them accordingly. Through performance evaluation, the effectiveness of the proposed scheme can be verified.