Video classification is a challenging task in computer vision. Although Deep Neural Networks (DNNs) have achieved excellent performance in video classification, recent research shows adding imperceptible perturbations to clean videos can make the well-trained models output wrong labels with high confidence. In this paper, we propose an effective defense framework to characterize and defend adversarial videos. The proposed method contains two phases: (1) adversarial video detection using temporal consistency between adjacent frames, and (2) adversarial perturbation reduction via denoisers in the spatial and temporal domains respectively. Specifically, because of the linear nature of DNNs, the imperceptible perturbations will enlarge with the increasing of DNNs depth, which leads to the inconsistency of DNNs output between adjacent frames. However, the benign video frames often have the same outputs with their neighbor frames owing to the slight changes. Based on this observation, we can distinguish between adversarial videos and benign videos. After that, we utilize different defense strategies against different attacks. We propose the temporal defense, which reconstructs the polluted frames with their temporally neighbor clean frames, to deal with the adversarial videos with sparse polluted frames. For the videos with dense polluted frames, we use an efficient adversarial denoiser to process each frame in the spatial domain, and thus purify the perturbations (we call it as spatial defense). A series of experiments conducted on the UCF-101 dataset demonstrate that the proposed method significantly improves the robustness of video classifiers against adversarial attacks.