Energy demand prediction plays an important role in sustainable development. The GM(1,1) model has drawn our attention to energy demand forecasting because it only needs a few data points to construct a time series model without statistical assumptions. Residual modification is often considered as well to improve the accuracy of predictions. Several residual modification models have been proposed, but they focused on residual sign estimation, whereas the FLNGM(1,1) model using functional-link net (FLN) can estimate the sign as well as the modification range for each predicted residual. However, in the original FLN, an activation function with an inner product assumes that criteria are independent of each other, so additivity might influence the forecasting performance of FLNGM(1,1). Therefore, in this study, we employ the FLN with a fuzzy integral instead of an inner product to propose a nonadditive FLNGM(1,1). Experimental results based on real energy demand cases demonstrate that the proposed grey prediction model performs well compared with other grey residual modification models that use sign estimation and the additive FLNGM(1,1).