A slime mould algorithm (SMA) is a new meta-heuristic algorithm, which can be widely used in practical engineering problems. In this paper, an improved slime mould algorithm (ESMA) is proposed to estimate the water demand of Nanchang City. Firstly, the opposition-based learning strategy and elite chaotic searching strategy are used to improve the SMA. By comparing the ESMA with other intelligent optimization algorithms in 23 benchmark test functions, it is verified that the ESMA has the advantages of fast convergence, high convergence precision, and strong robustness. Secondly, based on the data of historical water consumption and local economic structure of Nanchang, four estimation models, including linear, exponential, logarithmic, and hybrid, are established. The experiment takes the water consumption of Nanchang City from 2004 to 2019 as an example to analyze, and the estimation models are optimized using the ESMA to determine the model parameters, then the estimation models are tested. The simulation results show that all four models can obtain better prediction accuracy, and the proposed ESMA has the best effect on the hybrid prediction model, and the prediction accuracy is up to 97.705%. Finally, the water consumption of Nanchang in 2020–2024 is forecasted.