Cloud and fog computing architectures decentralize the computational demands of both users and interconnected IoT devices. With the tremendous increase in computational demands relayed to such architectures and to efficiently manage and utilize available computational power, exceptional methods should be deployed in scheduling relayed tasks on available computational resources. In this paper, an Improved Marine Predators Algorithm (IMPA) is utilized to tackle the task scheduling problem by optimizing makespan that in turn reduces execution time of a set of relayed tasks to a set of computational resources. Due to the complexity of the problem’s search space, the proposed algorithm addresses the initialization phases by starting the optimization process with a population that is widespread in the search space and further improves the exploitation phase of the original marine predators algorithm with the incorporation of Opposition-based Learning (OBL). Simulation experiments conducted using synthetic and real-trace workloads show that IMPA achieved an improvement in average makespan time of 1.75–68.31% for synthetic workloads, 2.35–66.33% for the HPC2N workload, 2.31–66.44% for the NASA iPSC workload and 0.27–66.13% for the GOCJ workload. Further experimentation proves that the proposed IMPA can improve the average Degree of Imbalancing (DI) among utilized computational resources by up to 73.54% when compared to the results achieved by AEOSSA, AdPSO, BAAEQRL, EMVO and MHDA that serve as state-of-art algorithms from the literature. This displays the superiority of IMPA in efficiently assigning tasks among computational resources whilst reducing resource standby time.