Grey prediction models play a significant role in forecasting energy demand, particularly the GM(1,1) model. To increase the prediction accuracy of the original GM(1,1) model, the corresponding residual GM(1,1) model is often recommended. However, the original and residual models that form the basis of the remnant grey prediction model are usually set up independently. In this work, we use a neural network to determine the degree to which a predicted value obtained from the original GM(1,1) model can be modified. A distinctive feature of our proposed prediction model is that the residual model is leveraged by providing a new adjustment mechanism for predicted values to maximize the prediction accuracy. The independent creation of a residual model is no longer required for the proposed model. The prediction accuracy of the proposed prediction models is verified using real energy demand cases. Experimental results showed that the proposed remnant GM(1,1) models perform well in comparison with other remnant GM(1,1) variants.