Residential electricity demand in Iran has been increased rapidly in recent years and it has an important role in household’s welfare. As electricity is not storable, optimal electricity generation in peak and off-peak period is so important. In this paper, we use panel and GMM method to estimate price and income elasticities of residential electricity demand in short run and long run by peak and off-peak periods for Tehran, Shahriar and Varamin for 2009-2013. Price and income elasticities of residential electricity demand in short run is lower than long run in both peak and off-peak periods. Cross-price elasticity of electricity demand in peak and off-peak is positive indicating electricity demand in peak and off-peak are substitutes. So price polices has an important role to shift electricity demand from peak to off-peak period.