Application processes have to be efficiently performed on servers in a cluster with respect to not only performance but also energy consumption. In this paper, we consider a process migration (MG) approach to energy-efficiently performing an application process on servers in a cluster. In this paper, we propose a model to estimate the energy consumption of a server to perform processes. First, a process is initiated on a server named home server in a cluster. A process performed on a current server is migrated to another server if the server is expected to consume a smaller amount of electric energy to perform the process than the current server in the estimation model. A process takes checkpoints and sends the checkpoints to the home server. If a process is faulty, the home server recreates the process on an operational server and the process is restarted on a state saved at a checkpoint most recently taken on the home server. In the evaluation, the total energy consumption of servers is shown to can be smaller in the MG algorithm than the other algorithms.