  In this paper, we develop an oscillation free local discontinuous Galerkin
(OFLDG) method for solving nonlinear degenerate parabolic equations. Following
the idea of our recent work [J. Lu, Y. Liu, and C.-W. Shu, SIAM J. Numer. Anal.
59(2021), pp. 1299-1324.], we add the damping terms to the 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
are established. The numerical experiments demonstrate that the proposed method
maintains the high-order accuracy and controls the spurious oscillations well.
