Class-imbalance is one of the most challenging problems in online learning due to its impact on the prediction capability of data stream mining models. Most existing approaches for online learning lack an effective mechanism to handle high-dimensional streaming data with skewed class distributions, resulting in insufficient model interpretation and deterioration of online performance. In this paper, we develop a cost-sensitive regularized dual averaging (CSRDA) method to tackle this problem. Our proposed method substantially extends the influential regularized dual averaging (RDA) method by formulating a new convex optimization function. Specifically, two $R$ 1 -norm regularized cost-sensitive objective functions are directly optimized, respectively. We then theoretically analyze CSRDA's regret bounds and the bounds of primal variables. Thus, CSRDA benefits from achieving a theoretical convergence of balanced cost and sparsity for severe imbalanced and high-dimensional streaming data mining. To validate our method, we conduct extensive experiments on six benchmark streaming datasets with varied imbalance ratios. The experimental results demonstrate that, compared to other baseline methods, CSRDA not only improves classification performance, but also successfully captures sparse features more effectively, hence has better interpretability.