An　abnormal　solution　might　occur　during　the　learning　process　of　echo　state　network　if　the　least　singular　value　of　reservoir　state　matrix　is　very　close　zero.　To　solve　this　problem,　an　echo　state　network　based　on　Levenberg-Marquardt　(LM-ESN)　algorithm　replacing　linear　regression　for　output　weights　is　proposed　and　a　new　damping　term　is　given.　In　the　proposed　method,　it　is　demonstrated　that　the　output　weights　sequence　has　quadratical　convergence　if　the　norm　of　error　vector　provides　a　local　error　bound.　Simulations　show　that　the　new　method　could　deal　with　abnormal　solution　problems　effectively,　also　it　has　better　performance　and　robustness　for　time　series　prediction　than　some　existing　methods.