The intensified contradiction between water resources and social development has restricted the development of the Yangtze River Delta. Due to the importance of water consumption in relieving this contradiction, this paper proposes a novel cumulative multivariable grey model with a high performance to predict the water consumption. Firstly, the grey correlation analysis is applied to study the influencing factors, and then the DGM(1,N) with deformable accumulation (DDGM(1,N) model) is constructed and used to predict the water consumption. The results show that the resident population has a significant impact on the water consumption, and the performance of the DDGM(1,N) model is better than the other two grey models. Secondly, the proposed novel grey model is applied to predict the water consumption in 17 cities in the Yangtze River Delta, and the predicted water consumption in Zhejiang and Shanghai indicates a downward trend, while the predicated water consumption in some cities of the Anhui Province presents an upward trend, such as Chizhou, Chuzhou, Wuhu and Tongling. Finally, some policy implications are provided that correspond to the population growth and three major industries in different situations. This paper enriches the research method and prediction analysis used for the water consumption, and the findings can provide some decision-making references for water resources management.