The theory of tunneling into an impurity band across a junction is developed by using the self-consistent Green's function in a ramdom array of impurity potential. If a short range potential is assumed for the impurity potential, the tunneling current density is expressed in terms of the proper self-energy Σ and the first and second derivatives of the current with respect to applied voltage are obtained. The results are examined numerically and it is shown that d 2 J /d V 2 - V curve should have a structure around the energy gap between the impurity band and the main band. In the impurity band, the d J /d V - V curve reflects the influence of Im Σ , while in the main band region it reflects the parabolic behaviour of the density of states because of the smaller contribution of Im Σ .