With the rapid development of mobile Internet and video applications, robust video watermarking technology has become a focal area of research for protecting and tracking intellectual property rights in digital media. An important characteristic of video is that it has both spatial and temporal properties. Previous studies in video watermarking have primarily focused on either spatial or temporal distortions and did not uniformly consider all types of video distortion, which restricts the robustness of video watermarking. In this paper, a novel robust blind video watermarking is proposed by exploring consistent spatio-temporal distortion and stable 3-D DCT coefficients. Our method achieves stronger robustness by uniformly treating the spatial and temporal distortions of the video. The properties of the stable 3-D DCT coefficients are mathematically proved, which makes the scheme generalizable. Extensive experiments have demonstrated that our method is resistant to video compression (H.264/AVC, H.265/HEVC) attacks, geometric attacks, and temporal domain attacks, and outperforms the current state-of-the-art video watermarking schemes.