Monitoring and predicting the displacement response of concrete dams is one of the critical activities that ensure their long‐term safe operation. The nonlinear interrelationships between dam displacements and their influencing factors make predictive modeling challenging. The majority of available studies focus strongly on improving the accuracy of point predictions of dam displacements, while ignoring the inherent uncertainties involved in dam systems. To quantify the uncertainties related to predictions, this study adopts the prediction intervals (PIs), rather than using point predictions, to estimate future displacements. An ensemble learning‐based interval prediction model, referred to as gradient boosted quantile regression (GBQR), is proposed to construct the PIs of dam displacements. This model integrates the classification and regression tree (CART) and quantile regression (QR) methodologies into a gradient boosting framework and outputs the optimal PIs by minimizing a differentiable loss function when adding trees. Specifically, multiple CART base‐learners are additively combined to model complex mappings between the inputs and the output. A redefined QR‐based pinball loss, replacing the squared error loss, is also derived to determine the upper and lower limits of the PIs. Throughout the whole process, we use a gradient descent procedure to guide the training of the model parameters. The final GBQR model is formulated in this way, and then the dam displacement PIs are directly generated. The developed GBQR model is verified using long‐term monitoring data of a real‐world concrete dam, and its performance is compared with various state‐of‐the‐art modeling methods. The results confirm that the proposed method performs better and can provide high‐quality PIs of dam displacements, thus assisting risk analysis and decision‐making. This novel model could be generalized for modeling and prediction of other types of structural behavior.