Destriping　has　attracted　a　lot　of　interest　in　the　field　of　remote　sensing　images　processing.　Recent　research　works　consider　the　characteristics　of　stripes,　among　which　low-rankness　and　group　sparsity　regularizations　are　widely　used.　However,　for　real　scenarios,　these　regularizations　sometimes　fail　to　work　when　the　underlying　assumptions　are　violated.　Motivated　by　this　observation,　we　propose　a　novel　and　flexible　regularization,　named　as　the　reweighted　block　sparsity　(RBS),　for　complex　stripes　(e.g.,　the　partial　stripes).　RBS　divides　the　stripe　layer　into　several　blocks　along　the　stripe-perpendicular　direction　and　boosts　the　group　sparsity　of　each　block,　where　the　sparsity　level　is　adaptively　controlled　by　updating　weights.　Based　on　RBS,　we　further　propose　a　destriping　model　by　integrating　RBS　and　unidirectional　total　variation　regularization,　which　can　better　detect　and　remove　complex　stripes.　Moreover,　we　develop　an　alternating　direction　method　of　multipliers　algorithm　to　solve　the　proposed　model.　Experimental　results　demonstrate　that　the　proposed　method　outperforms　the　state-of-the-art　competitors　qualitatively　and　quantitatively.