To improve prediction accuracy of top-coal drawing capability in steep seams, principal component analysis (PCA) and the general regression neural network (GRNN) are combined (PCA–GRNN model) to predict top-coal drawing capability in steep seams. Nine commonly used influencing factors are selected to establish a predictive index system for top-coal drawing capability in steep seams. The PCA is used to eliminate correlation and reduce dimensions of various indices, thus obtaining three linearly uncorrelated principal components (PCs) y1, y2, and y3, which form the input vectors of the GRNN. In this way, the factors that most affect the top-coal drawing capability in steep seams are found to be floor flatness, dip angle of the coal seam, and the hardness of the coal seam. The results show that the PCA–GRNN model outperforms the GRNN and random forest models in prediction results, which indicates that the PCA improves prediction accuracy of the GRNN model. It is feasible to predict top-coal drawing capability in steep seams by combining or even integrating different analytical models into one. The proposed PCA–GRNN model can be used to predict top-coal drawing capability in steep seams.