In the recent paper [Hideaki Kaneko, Kim S. Bey and Gene J. Hou, Discontinuous Galerkin finite element method for parabolic problems (2003) (submitted)], a discontinuous Galerkin time discretization scheme was developed for a class of parabolic partial differential equations. The non-uniform time discretization is based upon the a priori knowledge of the weak singularity of One of the goals of this paper is to generalize the results obtained in [Hideaki Kaneko, Kim S. Bey and Gene J. Hou, Discontinuous Galerkin finite element method for parabolic problems (2003) (submitted)] to a class of nonlinear parabolic equations. The nonlinear system of equations is solved by two different iterative methods and the corresponding error estimates are provided.