Accurate prediction of seepage discharge in earth-rock dams remains challenging due to the strong non-stationary and nonlinear characteristics, limited robustness of individual models, and poor interpretability of black-box approaches. To address these issues, this paper proposes an interpretable hybrid model that integrates Variational Mode Decomposition (VMD), Long Short-Term Memory (LSTM) networks, and Support Vector Machine (SVM). The model first decomposes the seepage discharge sequence and relevant lagged features using VMD. The LSTM network then captures temporal dependencies of the decomposed components, while the SVM performs regression on the original sequences and features. An adaptive fusion mechanism is established based on validation-set performance, using a 10% MAE-difference threshold selected from nearby candidate settings. Additionally, the SHapley Additive exPlanations (SHAP) framework is incorporated to quantify feature contributions. Experimental results demonstrate that the proposed model achieves MAE, root mean square error (RMSE), and mean absolute percentage error (MAPE) values of 0.0124 L/s, 0.0198 L/s, and 8.75%, respectively, outperforming the benchmark models, with $R^2$ improved to 0.9811. SHAP analysis further identifies reservoir water level as the most influential feature, contributing 37.5% to the predictions and showing broad consistency with engineering understanding of seepage behavior. By integrating VMD, LSTM, and SVM within an adaptive and interpretable workflow, this study enhances both predictive accuracy and interpretability, offering a reliable basis for anomaly diagnosis in earth-rock dam seepage monitoring.