This research introduces a technique for scheduling workflow applications, which considers various Quality of Service needs in cloud computing. The primary objective is to efficiently schedule a specific application onto the available machines in the cloud environment, minimizing total execution cost (TEC) and total execution time (TET) while maximizing resource usage and adhering to the Service Level Agreement between users and cloud providers. Workflow scheduling is an NP-hard problem with significant issues in cloud computing systems. The existing traditional algorithms cannot solve the workflow scheduling problem in polynomial time. This paper uses a modified grey wolf optimizer (MGWO) algorithm for the multi-objective model to solve the workflow scheduling problem in cloud computing because this algorithm has enhanced exploration capability. This algorithm was tried to decrease the TET and TEC of the interdependent tasks in cloud computing. The experimentation outcomes demonstrate that the MGWO algorithm bested the RR, ACO, and GWO algorithms regarding TET and TEC.