In order to accurately predict the variation in wax deposition thickness in crude o il pipelines and alleviate the shortcomings of the traditional grey model (GM) in model structure and data processing, a three-parameter grey model (TPGM) (1,1) has been constructed. The bald eagle search algorithm (BES) was improved in terms of initial population and Levy flight strategy. The improved bald eagle search algorithm (IBES) was used to automatically optimize the initial value and background value of the TPGM (1,1) model, and an optimization prediction model of pipeline wax deposition thickness based on IBES-TPGM (1,1,λ,η) was established. The wax deposition thickness data for the indoor loop and field pipeline were used for training and prediction. The prediction accuracies of different models were compared, and the influence of the number of data sets on the accuracy of the model was analyzed. Ablation experiments show that the IBES algorithm is superior to other algorithms in optimization accuracy, convergence speed and global search ability, and the improved strategy is of practical use. The average relative errors of the IBES-TPGM (1,1,λ,η) model on indoor loop experimental data and field pipeline data are the smallest, 0.6867% and 0.1527%, respectively. The prediction effect is better than that of GM (1,1), TPGM (1,1) and BES-TPGM (1,1,λ,η) models. The established model has low requirements for the number of training sets and is suitable for medium and long-term prediction of pipeline wax deposition thickness. This work provides a practical reference for the determination of pigging cycles and the safe operation of pipelines.