Concept drifts occurring in data streams will jeopardize the accuracy and stability of the online learning process. If the data stream is imbalanced, it will be even more challenging to detect and cure the concept drift. In the literature, these two problems have been intensively addressed separately, but have yet to be well studied when they occur together. In this paper, we propose a chunk-based incremental learning method called Dynamic Weighted Majority for Imbalance Learning (DWMIL) to deal with the data streams with concept drift and class imbalance problem. DWMIL utilizes an ensemble framework by dynamically weighting the base classifiers according to their performance on the current data chunk. Compared with the existing methods, its merits are four-fold: (1) it can keep stable for non-drifted streams and quickly adapt to the new concept; (2) it is totally incremental, i.e. no previous data needs to be stored; (3) it keeps a limited number of classifiers to ensure high efficiency; and (4) it is simple and needs only one thresholding parameter. Experiments on both synthetic and real data sets with concept drift show that DWMIL performs better than the state-of-the-art competitors, with less computational cost.