Abstract Employing cloud computing to acquire the benefit of cloud by optimizing various parameters that meet changing demands is a challenging task. The optimal mapping of tasks to virtual machines (VMs) and VMs to physical machines (PMs) (known as VM placement) problem are necessary for advancing energy consumption and resource utilization. High heterogeneity of tasks as well as resources, great dynamism and virtualization make the consolidation issue more complicated in the cloud computing system. In this paper, a complete mapping (i.e., task VM and VM to PM) algorithm is proposed. The tasks are classified according to their resource requirement and then searching for the appropriate VM and again searching for the appropriate PM where the selected VM can be deployed. The proposed algorithm reduces the energy consumption by depreciating the number of active PMs, while also minimizes the makespan and task rejection rate. We have evaluated our proposed approach in CloudSim simulator, and the results demonstrate the effectiveness of the proposed algorithm over some existing standard algorithms.