The expanded upwind-mixed method on dynamically changing meshes is presented for the positive semi-definite problem of two-phase miscible flow in porous media. The pressure is approximated by a mixed finite element method and the concentration is approximated by a method which upwinds the convection and incorporates diffusion using an expanded mixed finite element method. When the mesh changes, error estimate is derived under the assumption of only a positive semi-definite diffusion coefficient. Finally, the numerical experiments are given.