In　many　sparse　coding　based　image　restoration　and　image　classification　problems,　using　non-convex　ℓp-norm　minimization　(0　≤p　＜1)　can　often　obtain　better　results　than　the　convex　ℓ1-norm　minimization.　A　number　of　algorithms,　e.g.,　iteratively　reweighted　least　squares　(IRLS),　iteratively　thresholding　method　(ITM-ℓp),　and　look-up　table　(LUT),　have　been　proposed　for　non-convex　ℓp-norm　sparse　coding,　while　some　analytic　solutions　have　been　suggested　for　some　specific　values　of　p.　In　this　paper,　by　extending　the　popular　soft-thresholding　operator,　we　propose　a　generalized　iterated　shrinkage　algorithm　(GISA)　for　ℓp-norm　non-convex　sparse　coding.　Unlike　the　analytic　solutions,　the　proposed　GISA　algorithm　is　easy　to　implement,　and　can　be　adopted　for　solving　non-convex　sparse　coding　problems　with　arbitrary　p　values.　Compared　with　LUT,　GISA　is　more　general　and　does　not　need　to　compute　and　store　the　look-up　tables.　Compared　with　IRLS　and　ITM-ℓp,　GISA　is　theoretically　more　solid　and　can　achieve　more　accurate　solutions.　Experiments　on　image　restoration　and　sparse　coding　based　face　recognition　are　conducted　to　validate　the　performance　of　GISA.　©　2013　IEEE.