Gradient-boosted decision trees (GBDT) are widely used and highly effective machine learning approach for tabular data modeling. However, their complex structure may lead to low robustness against small covariate perturbation in unseen data. In this study, we apply one-hot encoding to convert a GBDT model into a linear framework, through encoding of each tree leaf to one dummy variable. This allows for the use of linear regression techniques, plus a novel risk decomposition for assessing the robustness of a GBDT model against covariate perturbations. We propose to enhance the robustness of GBDT models by refitting their linear regression forms with $L_1$ or $L_2$ regularization. Theoretical results are obtained about the effect of regularization on the model performance and robustness. It is demonstrated through numerical experiments that the proposed regularization approach can enhance the robustness of the one-hot-encoded GBDT models.