In　this　paper,　we　propose　a　new　method　of　designing　and　constructing　＂good＂　mappings　defined　by　kernel　functions　for　classification　task,　called　Optimal　Successive　Mappings　(OSM).　Kernel　methods,　such　as　Support　Vector　Machines　(SVM),　could　not　provide　satisfactory　classification　accuracy　on　some　complicated　data　sets,　which　are　still　not　linearly　separable　in　feature　space.　It　means　kernels　designed　only　by　tuning　kernel　parameters　cannot　adapt　well　to　classification　of　complicated　data　sets.　Unlike　tuning　parameters,　OSM　learns　and　designs　its　kernel　from　training　data,　through　a　sequence　of　two　mappings　and　optimizing　a　criteria　function.　After　feature　mapping　of　OSM,　data　in　the　feature　space　appear　not　only　linearly　separable　but　also　intra-class　compact　and　extra-class　separate.　As　the　problem　of　optimizing　the　criteria　function　reduces　to　a　generalized　eigenvalue　problem,　OSM　possesses　non-iterative　and　low　complex　properties.　Comparative　experiments　demonstrate　the　effectiveness　of　our　method.