Internet of Things (IoT) tasks have a variety of quality of service (QoS) needs, wherein the fog-cloud computing has emerged as a promising platform for handling the tasks. As a result of its proximity to IoT devices, the fog environment offers minimal latency, but it also faces resource limitations, which is not present in cloud environment. The key obstacle of the fog-cloud setting is effectively executing tasks delegated from IoT devices, by making use of the available resources in the fog-cloud infrastructure. Hence, this research introduces a novel task scheduling approach based on the improved meta-heuristic algorithm. An improved zebra algorithm (ImZP) is proposed for performing the priority aware task scheduling. The zebra algorithm is hybridized with the mutation operation of the differential evolution algorithm (DE) for enhancing the exploration criteria to accomplish the global best solution. Besides, the acquisition of non-dominant solutions while considering the multi-objective fitness function, pareto optimal front is considered. Here, the multi-objective function based on priority, cost and execution time are considered in scheduling the task optimally. The assessment of priority aware task scheduling based on priority, availability, makespan, energy consumption, cost and success rate acquired the values of 0.9787, 0.8236, 0.1049, 0.0244, 0.1095 and 0.8238 respectively.