Multispectral　images　(MSIs)　contain　more　spectral　information　than　traditional　2D　images,　which　can　provide　a　more　accurate　representation　of　objects.　MSIs　are　easily　affected　by　various　noises　when　captured　by　sensors.　In　recent　years,　many　MSI　denoising　methods,　especially　the　Kronecker-basis-representation　(KBR)　method,　have　achieved　great　success.　KBR　uses　tensor　representation　and　decomposition　to　achieve　good　MSI　denoising　performance.　However,　each　full　band　patch　(FBP)　group　is　decomposed　in　this　method　so　that　too　many　dictionary　atoms　are　generated.　In　this　paper,　we　propose　a　structural　tensor　sparsity　promoting　(STSP)　model　for　MSI　denoising.　In　order　to　decrease　the　number　of　dictionary　atoms,　we　cluster　FBP　groups　and　learn　orthogonal　dictionaries　for　each　class　rather　than　each　FBP　group.　To　improve　the　denoising　performance,　the　structural　similarity　among　FBP　groups　are　utilized　in　the　STSP　model　by　enforcing　nonlocal　centralized　sparse　constraint,　where　the　compromise　parameter　is　statistically　and　adaptively　determined.　Experimental　results　on　the　the　CAVE　dataset　demonstrate　that　our　model　outperforms　the　state-of-art　methods　in　terms　of　both　objective　and　subjective　quality.　©　2022　ACM.