An　oscillation　free　local　discontinuous　Galerkin　(OFLDG)　method　is　proposed　for　solving　nonlinear　degenerate　parabolic　equations.　The　damping　terms　are　added　to　the　original　LDG　scheme　to　control　the　spurious　oscillations　when　solutions　have　a　large　gradient.　The　L-2-stability　and　optimal　priori　error　estimates　for　the　semi-discrete　scheme　in　one-　and　multi-dimensions　are　established.　The　numerical　experiments　demonstrate　that　the　proposed　method　maintains　the　high　order　accuracy　and　controls　the　spurious　oscillations　well.