ABSTRACTThe task of tensor (matrix) completion has been widely used in the fields of computer vision and image processing, etc. To achieve the completion, the existing methods are mostly based on singular value decomposition of the real tensors and nuclear norm minimization. However, the real tensor completion methods cannot simultaneously maintain color channel correlation and evolution robustness of color video frames, and they need high computational costs to handle the high‐dimensional data. Hence they have some limitations in model generalization ability and computational efficiency. In this article, a new completion method for the quaternion tensor (matrix) is explored via the QR decomposition and the definition of novel quaternion tensor norm, which can well balance the model generalization ability and efficiency, and the performance of the completion method has been substantially improved. Numerical experiments on color images and videos prove the effectiveness of our proposed method.