It is difficult to extract appropriate features of blurry digital video because of the low quality image for which traditional forgery detection methods are not effective. The video is often blurred due to various complicated conditions, such as limited bandwidth or low pixel complementary metal oxide semiconductor sensors. To address the feature extraction problem for blurry video, we explore one low rank theory to deblur video, which fuses multiple fuzzy kernels of key frame images by low rank decomposition. Further, we extract mean structural similarity features and information fidelity criterion features sequentially by the double detection mechanism to detect forgery points on blurred video frames. We can determine the forgery form of the video and locate the source replication area of the copy-move forgery. Experimental evaluation on two public video databases and videos that we recorded show that this method is robust in blurry video forgery detection, and compared with traditional video forgery detection methods, the efficiency is improved.