Residential demand forecasting is affected by multiple factors and is non-linear. To address this issue, the study modifies the original neighborhood rough set (NRS) and then combines it with extreme learning machines (ELMs) to forecast residential demands. Specifically, the modified NRS (MNRS) algorithm constructs a neighborhood relationship matrix based on the neighborhood radii and standard deviations of different conditional attributes, thereby overcoming the failure of the original NRS algorithm to set the optimal neighborhood value for different conditional attributes. Then, the Pearson correlation coefficient is introduced into output attribute importance ranking to overcome the influence among conditional attributes, and the minimal redundant attribute-based reduction set is obtained to serve as the indicator system for residential demand forecasting. Finally, the residential demand indicator system is input into the ELM model to output an accurate forecasted value. Experimental results show that the MNRS-ELM forecasting model not only effectively reduces the operational complexity but also achieves higher prediction accuracy.