Semi-supervised　kernel　learning　is　an　important　technique　for　classification　and　has　been　actively　studied　recently.　In　this　paper,　we　propose　a　new　semi-supervised　spectral　kernel　learning　method　to　learn　a　new　kernel　matrix　with　both　labeled　data　and　unlabeled　data,　which　tunes　the　spectral　of　a　standard　kernel　matrix　by　maximizing　the　margin　between　two　classes.　Our　approach　can　be　turned　into　a　non-linear　optimization　problem.　We　use　lagrangian　support　vector　machines　and　gradient　descent　algorithm　together　to　solve　our　optimization　problem　efficiently.　Experimental　results　show　that　our　spectral　kernel　learning　method　is　more　effective　for　classification　than　traditional　approaches.　©　2010　IEEE.