Since most of the previous video watermark algorithms regard a video as a series of consecutive images, the embedding and extraction of watermark are performed on these images, and the correlation and redundancy among frames of a video are not considered. Such algorithms are weak in protecting against frame attacks. In order to improve the robustness, we take into consideration the correlation and redundancy among the frames of a video to propose a blind video watermark algorithm based on tensor decomposition. First, a grayscale video is represented as a 3-order tensor, and the core tensor is obtained by tensor decomposition. Second, the watermark embedding position is selected based on the stability of the maximum value in the core tensor because the core tensor represents the main energy of a video. Then, the watermark is embedded by quantifying the maximum value in the core tensor. Finally, the watermark is uniformly distributed across frames of a video by inverse tensor decomposition. The experiments show that our algorithm based on tensor decomposition has better imperceptibility and robustness against common video attacks.