Tracking concept drifts in data streams has recently become a hot topic in data mining. Most of the existing work is built on a single-window-based mechanism to detect concept drifts. Due to the inherent limitation of the single-window-based mechanism, it is a challenge to handle different types of drifts. Motivated by this, a new classification algorithm based on a double-window mechanism for handling various concept drifting data streams (named DWCDS) is proposed in this paper. In terms of an ensemble classifier in random decision trees, a double-window-based mechanism is presented to detect concept drifts periodically, and the model is updated dynamically to adapt to concept drifts. Extensive studies on both synthetic and real-word data demonstrate that DWCDS could quickly and efficiently detect concept drifts from streaming data, and the performance on the robustness to noise and the accuracy of classification is also improved significantly.