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. So a basic problem of the fog-cloud environment is the execute tasks that are offloaded from IoT devices by effectively using the fog-cloud resources. 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 analysis of ImZP show superior performance over the existing algorithims in terms of the metrics like priority, availability, makespan, energy consumption, cost and success rate. The values obtained are respectively 0.9702%, 0.7436%, 0.00567 ms, 0.03066 J, 0.04171G$ and 0.7438.