Nowadays, construction waste has become a global challenge that needs to be addressed, and its accurate prediction is crucial for subsequent treatment and policy development. However, current popular big data methods struggle to be effectively applied due to sample size limits. Meanwhile, the key issues of data uncertainty and time-delayed nature must be considered, the former of which can be addressed by interval prediction. Therefore, a novel interval time-delayed three-parameter discrete grey model for construction waste prediction is proposed in this study, whose time-delayed coefficient is optimized via optimization algorithms. Moreover, the relevant mathematical derivation and proof of this model are also described and discussed in detail in the research. Two case studies of the construction waste dataset are used to examine the effectiveness of the proposed model. Through a series of comparisons with other state-of-the-art models, the results show that the proposed model can improve the prediction performance with excellent prediction results. Meanwhile, this study also presents scenario analysis and discussions of the construction waste prediction results during the 14th Five-Year Plan period, and finds that the current policies and measures are difficult to achieve the future planning goals, and further policy development and implementation of measures are imminent.