Blind　single-image　super-resolution　refers　to　reconstructing　the　high-resolution　image　from　a　single　low-resolution　one　with　an　unknown　blur　kernel,　which　is　a　severely　ill-posed　inverse　problem.　The　additional　information　about　the　latent　high-resolution　image　can　be　incorporated　by　adding　the　regularizer　in　order　to　recover　or　reconstruct　reasonable　high-frequency　details　for　the　low-resolution　image.　In　this　paper,　we　propose　a　blind　super-resolution　method　based　on　the　cross-scale　low　rank　prior　from　a　single　low-resolution　image,　which　alternates　between　updating　the　blur　kernel　and　the　high-resolution　image　by　a　jointly　modeling　approach.　According　to　the　self-similarity　across　the　high-resolution　image,　the　low-resolution　image　and　its　down-sampled　image,　we　search　for　similar　patches　from　the　down-sampled　image　for　the　low-resolution　patch,　and　group　into　a　matrix　the　cross-scale　similar　image　patches　consisting　of　the　parents　of　the　low-resolution　patch　and　its　similar　patches　in　the　high-resolution　reconstructed　image　and　the　low-resolution　image　respectively.　Since　the　cross-scale　similar　patches　in　the　low-resolution　image　provide　potential　details　for　reconstructing　the　high-resolution　image　patches,　the　low　rank　matrix　approximation　applied　to　the　cross-scale　similar　patches　enforces　the　reconstructed　image　to　recover　more　high-frequency　details　and　thus　promotes　the　accuracy　of　the　kernel　estimation　during　the　iteration.　In　addition,　the　low　rank　regularization　elegantly　indicates　the　non-local　structure　of　data　inherently　robust　to　noise.　Experimental　results　on　real　and　simulated　images　show　that　the　proposed　method　can　accurately　estimate　the　blur　kernel　and　reconstruct　high-resolution　image　with　sharp　edges　and　fine　details,　which　outperforms　the　existing　blind　super-resolution　methods　based　on　unsupervised　learning.　©　2024　Chinese　Institute　of　Electronics.　All　rights　reserved.