<p>The hybrid Fog–cloud systems are considered one of the most effective systems in terms of servicing the Internet of Things (IoT). In such systems, IoT nodes offload tasks that require a large number of resources to be processed to nearby fog nodes or to the cloud servers. These tasks are processed in the fog nodes or in the cloud server and the result is returned to the IoT nodes. Of course, tasks with different requirements are generated by IoT nodes and offloaded to nearby fog nodes, which may lead to a variation in the load between fog nodes. The load variance is that some fog nodes serve a large number of tasks while other fog nodes are inactive or semi-inactive. An imbalance in the load results in a delay in the execution of tasks, some of which may be sensitive to delay. In this paper, we present a model of a hybrid cloud–fog system for task offloading distribution among fog nodes. We propose a new approach to distribute tasks between fog nodes, and we also provide a definition of the load balance that is consistent with the proposed system. The load distribution problem is addressed using a Quadratic Binary Integer Programming (QBIP)–based optimization framework that minimizes load disparities among fog nodes by optimally assigning tasks according to both the current status of fog nodes and the requirements of the tasks. The performance of the proposed algorithm is compared with two similar models that distribute the load between fog nodes, and the simulation results show the superiority of the proposed in terms of load balancing.</p>