The importance of forecasting in the electricity industry cannot be over emphasized. It is one of the most important planning tools that helps in the assessment and prediction of future power demand. Unfortunately precise forecasting is impossible and to tie the future plans too rigidly to future projection or forecast, no matter how sophisticated, is to risk costly mistakes. The simple exponential smoothing model and the box-Jenkins model are used to forecast electricity demand in Nigeria for the next twenty years. The high accuracy of the techniques is demonstrated by doing a forecast for past years and comparing the result with figures obtained from Power Company of Nigeria.