A local discontinues Galerkin finite element method for the numerical simulation of a convection-dominated equation in porous media with singular coefficient is studied in this paper，and the scheme of the local discontinuous method is given in detail for the singular equation studied. By rewriting the original equation into proper form and introducing the convective and diffusive numerical fluxes，the method can effectively overcome numerical oscillation occurred in case of convection-dominated problems. Numerical results are also given to show the effectiveness of the method.