We present a numerical scheme for solving the coupled system of incompressible miscible displacement problem in porous media. The flow equation is solved by the mixed finite element method, and the transport equation is approximated by a local discontinuous Galerkin method. Then the local discontinuous Galerkin method for flow and transport is introduced for the coupled system of compessible miscible displacement problem. Optimal error estimates in L∞ (L2 ) for concentration and in L∞ (L2 ) for velocity are derived.