Energy demand is an important economic index, and demand forecasting has played a significant role in drawing up energy development plans for cities or countries. As the use of large datasets and statistical assumptions is often impractical to forecast energy demand, the GM(1,1) model is commonly used because of its simplicity and ability to characterize an unknown system by using a limited number of data points to construct a time series model. This paper proposes a genetic-algorithm-based remnant GM(1,1) (GARGM(1,1)) with sign estimation to further improve the forecasting accuracy of the original GM(1,1) model. The distinctive feature of GARGM(1,1) is that it simultaneously optimizes the parameter specifications of the original and its residual models by using the GA. The results of experiments pertaining to a real case of energy demand in China showed that the proposed GARGM(1,1) outperforms other remnant GM(1,1) variants.