Based on the measured settlement data from the Reclamation Project of Eastern Hengsha Shoal, two improved BP neural networks optimized by the particle swarm optimization (PSO) algorithm and genetic algorithm (GA) respectively are employed to predict the long-term consolidation settlement of the dredged soil in the reclamation area. By comparing the prediction results of the improved neural networks with those obtained from standard BP neural network and various curve fitting methods including hyperbola method, Hoshino method, and Asaoka method, as well as field-measured data, the improved neural network methods are validated to have a better predictive performance. The error analysis results indicate that compared with the standard BP neural network and curve-fitting prediction methods, the improved BP neural networks exhibit smaller prediction errors in terms of MAE, MSE, RMSE, MAPE, etc., and have a closer match between the predicted settlement values and the actual values. The selected GA-BP and PSO-BP neural network prediction methods in this study demonstrate higher prediction accuracy. Meanwhile, GA-BP demonstrates higher prediction accuracy and generalization ability than PSO-BP, but PSO-BP shows faster convergence in terms of prediction speed. The preferred methods presented in this paper exhibit good robustness and high reliability, which can achieve accurate prediction of dredged soil settlement. Additionally, unlike the traditional curve-fitting methods, the selected methods can effectively reduce the influence of subjective factors during the settlement prediction, and provide a new approach for settlement prediction, which can be effectively utilized as a substitute for long-term settlement monitoring and give reference for the design of settlement control of foundation of further construction projects.