Due to the increasing of power consumption, it is difficult to construct accurate prediction model for daily peak power demand. It is very important work to know power demand in next day for manager and control power system. In this research, we develop a daily peak power demand prediction method considering of characteristics of day of week. The proposed method is composed of liner model based on AR model and nonlinear model based on ELM to resolve the limitation of a single model. Using data sets between 2006 and 2010 in Korea, the proposed method has been intensively tested. As the prediction results, we confirm that the proposed method makes it possible to effective estimate daily peak power demand than conventional methods.