In our rapidly-growing big-data area, often the big sensory data from Internet of Things (IoT) cannot be sent directly to the far data-center in an efficient way because of the limitation in the network infrastructure. Fog computing, which has increasingly gained popularity for real-time applications, offers the utilization of local mini data-centers near the sensors to release the burden from the main data-center, and to exploit the full potential of cloud-based IoT. In this paper, a high-performance approach based on the Max–Min Ant System (MMAS), which is an efficient variation in the family of ant colony optimization algorithms, is proposed to tackle the static task-graph scheduling in homogeneous multiprocessor environments, the predominant technology used as mini-servers in fog computing. The main duty of the proposed approach is to properly manipulate the priority values of tasks so that the most optimal task-order can be achieved. Leveraging background knowledge of the problem, as heuristic values, has made the proposed approach very robust and efficient. Different random task-graphs with different shape parameters have been utilized to evaluate the proposed approach, and the results show its efficiency and superiority versus traditional counterparts from the performance perspective.