Natural　image　modeling　plays　a　key　role　in　many　vision　problems　such　as　image　denoising.　Image　priors　are　widely　used　to　regularize　the　denoising　process,　which　is　an　ill-posed　inverse　problem.　One　category　of　denoising　methods　exploit　the　priors　(e.g.,　TV,　sparsity)　learned　from　external　clean　images　to　reconstruct　the　given　noisy　image,　while　another　category　of　methods　exploit　the　internal　prior　(e.g.,　self-similarity)　to　reconstruct　the　latent　image.　Though　the　internal　prior　based　methods　have　achieved　impressive　denoising　results,　the　improvement　of　visual　quality　will　become　very　difficult　with　the　increase　of　noise　level.　In　this　paper,　we　propose　to　exploit　image　external　patch　prior　and　internal　self-similarity　prior　jointly,　and　develop　an　external　patch　prior　guided　internal　clustering　algorithm　for　image　denoising.　It　is　known　that　natural　image　patches　form　multiple　subspaces.　By　utilizing　Gaussian　mixture　models　(GMMs)　learning,　image　similar　patches　can　be　clustered　and　the　subspaces　can　be　learned.　The　learned　GMMs　from　clean　images　are　then　used　to　guide　the　clustering　of　noisy-patches　of　the　input　noisy　images,　followed　by　a　low-rank　approximation　process　to　estimate　the　latent　subspace　for　image　recovery.　Numerical　experiments　show　that　the　proposed　method　outperforms　many　state-of-the-art　denoising　algorithms　such　as　BM3D　and　WNNM.