As　an　advanced　spectral　imaging　technology,　hyperspectral　has　critical　applications　in　remote　sensing.　Unfortunately,　hyperspectral　images　(HSIs)　are　frequently　contaminated　by　diverse　noise　interference　during　capture.　It　is　desirable　to　remove　these　mixed　noises　and　recover　clean　HSIs　accurately.　Current　approaches　struggle　to　deliver　great　performance　because　they　fail　to　effectively　utilize　the　spectral　correlations　in　hyperspectral　data.　This　paper　introduces　an　innovative　hyperspectral　image　denoising　algorithm　based　on　the　tensorial　weighted　Schatten-p　norm　and　graph　Laplacian　regularization　named　TWSPGLR.　Firstly,　to　improve　the　accuracy　of　low-rank　tensor　recovery,　the　tensorial　weighted　Schatten-　p　norm　is　introduced　to　recover　clean　hyperspectral　data.　Secondly,　we　introduce　a　spectral　constraint　to　enhance　restoration　accuracy　by　efficiently　exploiting　the　spectral　correlations　of　hyperspectral　data.　Finally,　experimental　results　demonstrate　the　superiority　of　TWSPGLR　compared　with　the　state-of-the-art　methods　for　HSI　denoising.　©　2025　IEEE.