A workflow consists of dependent tasks, and scheduling of a workflow in a cloud environment means the arrangement of tasks of the workflow on virtual machines (VMs) of the cloud. By increasing VMs and the diversity of task size, we have a huge number of such arrangements.Finding an arrangement with minimum completion time among all of the arrangements is an Non-Polynomial-hard problem. Moreover, the problem becomes more complex when a scheduling should consider a couple of conflicting objectives. Therefore, the heuristic algorithms have been paid attention to figure out an optimal scheduling. This means that although the singleobjective optimization, ie, minimizing completion time, proposes the workflow scheduling as an NP-complete problem, multiobjective optimization for the scheduling problem is confronted with a more permutation space because an optimal trade-off between the conflicting objectives is needed. To this end, we extended a recent heuristic algorithm called Grey Wolf Optimizer (GWO) and considered dependency graph of workflow tasks. Our experiment was carried out using the WorkflowSim simulator, and the results were compared with those of 2 other heuristic task scheduling algorithms.to optimize some conflicting objectives stated previously in the cloud computing environment. We called it Pareto-based GWO (PGWO) and evaluated its performance on 2 patterns of workflows.Similar to the PSO algorithm, the GWO algorithm is based on swarm intelligence proposed by Mirjalili et al. 6 To evaluate the performance of the proposed algorithm practically, we implemented the extend algorithm using the WorkflowSim tool, 7 which is based on the CloudSim tool. Results of the proposed algorithm were compared with those of Strength Pareto Evolutionary Algorithm 2 (SPEA2) algorithm. 8The rest of the article is organized as follows. In Section 2, related work is presented in the greedy, single, and multiobjectives categories.In Section 3, first we introduce the concept of task scheduling and then we present our method in 2 parts, the extension of (1) the single-objective optimization to multiobjective optimization (MOO) and (2) the GWO algorithm for support of MOO. In Section 4, experimental results, simulation environment, performance indices, and results of the proposed algorithm are evaluated. Finally, conclusions are drawn in Section 5.