Abstract: Parametric roll is a severe rolling motion that occurs in longitudinal waves, especially in head/quartering seas. This self-excited resonance phenomenon can lead to container falling overboard, equipment damage, and even capsize of the ship. Traditional numerical simulation methods based on hydrodynamics for calculating ship parametric roll face challenges such as high computational costs, demanding operational requirements, and an inability to cover all loading conditions. To address these issues, an integrated machine learning alternative model combining Agglomerative Hierarchical Clustering (AHC) and an improved Random Forest (RF) is proposed for efficiently predicting the amplitude of ship parametric roll. Utilizing HAC to compress feature dimensions, reduce model complexity, and lower computational costs; employing Particle Swarm Optimization (PSO) for global optimization of RF hyperparameters. The validation results based on hydrodynamic numerical simulation data from multiple operating conditions of a large container ship indicate that, compared to the Generalized Regression Neural Network (GRNN) and the unoptimized RF model, the proposed model (AHC-SPO-RF) achieves an average improvement of 5.84% and 0.27% in the determination coefficient (R²) for predicting the significant values of roll and pitch, respectively, and an average reduction of 59.28% and 10.69% in the root mean square error (RMSE), demonstrating superior prediction accuracy. Additionally, although the model training time is higher than that of benchmark machine learning methods, it is significantly less than hydrodynamic numerical simulation, providing a notable efficiency advantage in batch prediction tasks and proving its practical engineering value as an efficient alternative.