To　quickly　solve　online　support　vector　regression　algorithm,　an　algorithm　of　online　incremental　learning　which　based　on　Lagrangian　support　vector　regression　(LSVR)　was　proposed.　Unconstrained　optimization　problems　of　LSVR　could　be　solved　by　a　rapid　iterative　algorithm.　It　could　converge　from　any　starting　point.　LSVR　had　the　advantage　that　its　solution　was　obtained　by　taking　the　inverse　of　a　matrix　of　order　equaled　to　the　number　of　input　samples　plus　one　at　the　beginning　of　the　iteration.　The　incremental　learning　algorithm　of　LSVR　was　presented　by　using　the　S-M-W　identity　to　reduce　the　computing　time　in　the　linear　case.　As　for　the　nonlinear　case,　the　inversion　of　the　matrix　after　increment　was　solved　based　on　the　previous　computed　information　and　it　was　unnecessary　to　repeat　the　computing　process.　The　effectiveness　of　the　proposed　method　was　illustrated　with　several　data　sets.　Results　show　that　the　proposed　algorithm　compared　with　the　previous　algorithm　not　only　maintains　better　accuracy,　but　also　greatly　shortens　the　training　time.