Fog computing is a distributed computing model that can utilise the storage, analysis and processing capabilities of fog nodes near edge devices. Although fog computing can support task processing for various Internet of Things (IoT) systems, Fog-IoT architecture faces several new challenges with the rapid development of IoT systems, especially delay-sensitive IoT systems, such as stochastic and dynamic data arrival, optimal utility and deadline of tasks. To address these challenges, workload scheduling toward worst-case delay and optimal utility for single-hop Fog-IoT architecture are studied and the workload dynamic scheduling algorithm (WDSA) is proposed. The proposed WDSA algorithm can maximise the average throughput utility while guarantees the worst-case delay of task processing. In addition, it is online and needs no prior information about future. The algorithm performance is analysed from the perspective of optimality and worst-case delay, demonstrating that the proposed WDSA algorithm can get an approximate optima and worst-case delay guarantees. Finally, simulation results demonstrate that the efficiency and efficacy of this kind of the algorithm can meet the requirement.