The wear of backup rolls will have a great impact on the quality of hot rolled strip sheet shape. In order to overcome the limitations of the finite element method (FEM) in calculating the wear of backup rolls in terms of efficiency and accuracy, this paper proposes a FEM+ML tandem hybrid model to optimise the prediction effect of the finite element method (FEM) on the wear of backup rolls. Firstly, a backup roller wear model is established based on FEM. Secondly, in order to select the optimal machine learning (ML) algorithm as the finite element error compensation model, three types of finite element error compensation models were established based on the random forest (RF) algorithm, radial basis neural network (RBF) algorithm, and particle swarm optimisation support vector machine (PSO-SVM) algorithm. Finally, the three types of finite element error compensation models were connected in series with the FEM model to compare the prediction performance of the three types of FEM+ML models on the wear of backup rolls. The numerical experimental results show that the FEM+PSO-SVM model can predict the wear of the backup roll better, and the PSO-SVM algorithm is most suitable for establishing the finite element error compensation model. It is proved that the FEM+ML model proposed in this paper can effectively improve the accuracy and computational efficiency of the FEM model for predicting the wear of the backup rolls without adding microelements. In addition, among the hot rolling parameters, the rolling force has the greatest influence on the wear of the backup rolls, and excessive rolling force should be avoided for a single pass in order to slow down the wear of the backup rolls.