In this paper, we investigate the influence of a gate electric field on the tunneling current for the contact of impurity graphene nanoribbon with a metal or quantum dots. Based on the Hamiltonian for graphene in the tight-binding approximation, the density of states is calculated, which allows us to obtain a tunneling current. We analyze the effect of the field magnitude on the detecting possibility of an impurity in the graphene nanoribbon. A sufficient change of current–voltage characteristic (CVC) of the contact is observed, with an increase in the constant electric field applied parallel to the nanoribbon plane.