The build-up rate prediction is of great importance for trajectory control in the field of drilling. However, it is very difficult to achieve accurate prediction due to the complexity, nonlinearity, and multiple uncertainties of the drilling system. As a consequence, a novel hybrid prediction model is proposed, which uses multiple feature selection methods, the model combination strategy based on machine learning, and three prediction models to improve the prediction accuracy of the build-up rate. More precisely, correlation analysis, importance analysis, and statistical analysis are employed to ensure the effectiveness of feature selection. Then, a novel classification prediction model called SVM-SVR is proposed to improve the accuracy of samples with the higher build-up rate. Subsequently, the SVR optimized by grey wolf optimizer (GWO-SVR) and back propagation (BP) neural network are constructed. Finally, the three models are integrated by a weighted combination method based on SVR to realize the accurate prediction of the build-up rate. To verify the performance of the hybrid model, the data of the Z48 well in Sichuan province is used, and the results show that the hybrid model can reduce by 22.7% in mean absolute error (MAE) and 32% in mean square error (MSE) when compared with the existing models.