In　this　paper,　efficient　algorithms　are　proposed　to　perform　sparse　coding　for　the　features　lifted　to　a　high-dimensional　space　via　nonlinear　mapping.　we　developed　how　the　well-known　sparse　coding　algorithm　Homotopy　Iterative　Thresholding(HIHT)　algorithm　can　be　made　nonlinear　with　the　kernel　method.　We　also　put　forward　the　corresponding　dictionary　learning　strategy　using　the　Lagrange　dual　method.　The　experimental　results　we　tested　prove　that　the　application　of　the　kernel　sparse　coding　in　the　classification　problem　is　significantly　improved　compared　with　their　linear　counterparts.　©　2018　IEEE.