With tremendous increase in Internet capacity and services, the demand for cloud computing has also grown enormously. This enormous demand for cloud based data storage and processing forces cloud providers to optimize their platforms and facilities. Reducing energy consumption while maintaining service level agreements (SLAs) is one of the most important issues in this optimization effort. Dynamic virtual machine allocation and migration is one of the techniques to achieve this goal. This technique requires constant measurement and prediction of usage of machine resources to trigger migrations at right times. In this thesis, we present a dynamic virtual machine allocation and migration method utilizing CPU usage prediction to improve energy efficiency while maintaining agreed quality of service levels in cloud datacenters. Our proposed method, called LRAPS, tries to estimate short-term CPU utilization of hosts based on their utilization history. This estimation is then used to detect overloaded and underloaded hosts as part of live migration process. If a host is overloaded, some of the VMs running on that host are migrated to other hosts to avoid SLA violations; if a host is underloaded, all of the VMs in that host are tried to be migrated to other machines so that the host can be powered off. We did extensive simulation experiments using CloudSim to evaluate the efficiency and effectiveness of our proposed method. Our simulation experiments show that our method is feasible to apply and can signi cantly reduce power consumption and SLA violations in cloud systems.