<p>Cloud computing offers on-demand services via the Internet. Workflow scheduling is an <i>np</i>-hard and complex optimization problem for cloud computing. Most existing algorithms for conventional platforms struggle to find polynomial-time solutions for workflow scheduling. Specific meta-heuristic algorithms proposed in the past for the workflow scheduling problem cannot provide the global optimal solution because they are trapped in the local optimal solution. This paper proposes the PSO-MGWO algorithm for workflow scheduling, combining modified grey wolf optimization (MGWO) and particle swarm optimization (PSO). The PSO-MGWO algorithm not only overcomes the limitations of past algorithms but also offers the potential to significantly reduce the dependents’ total execution time (<i>TET</i>) and total executing cost (<i>TEC</i>). The PSO-MGWO algorithm is a hybrid approach for workflow scheduling. It reduces the <i>TEC</i> and <i>TET</i> of dependent tasks in cloud computing. Unlike the standard PSO and MGWO algorithms, the PSO-MGWO algorithm does not adhere to local optimal solutions. Experimental results demonstrate that the PSO-MGWO performs better in terms of <i>TEC</i> and <i>TET</i>.</p>