As an excellent ensemble algorithm, Gradient Boosting Decision Tree (GBDT) has been tested extensively with static data. However, real-world applications often involve dynamic data streams, which suffer from concept drift problems where the data distribution changes overtime. The performance of GBDT model is degraded when applied to predict data streams with concept drift. Although incremental learning can help to alleviate such degrading, finding a perfect learning rate (i.e., the iteration in GBDT) that suits all time periods with all their different drift severity levels can be difficult. In this paper, we convert the issue of determining an optimal learning rate into the issue of choosing the best adaptive iterations when tuning GBDT. We theoretically prove that drift severity is closely related to the convergence rate of model. Accordingly, we propose a novel drift adaptation method, called adaptive iterations (AdIter), that automatically chooses the number of iterations for different drift severities to improve the prediction accuracy for data streams under concept drift. In a series of comprehensive tests with seven state-of-the-art drift adaptation methods on both synthetic and real-world data, AdIter yielded superior accuracy levels.