There exist a few works concerning the soft imperfect interface characterized by the discontinuity of displacements. Actually, there is another type of imperfect interface, namely the stiff imperfect interface. In this work, the model of stiff imperfect interface is proposed. Then the interaction of a screw dislocation with stiff imperfect interface is studied. The force acting on a screw dislocation due to the presence of the stiff imperfect interface is formulated. The results show that the interacting force varies between that for a rigid contact interface and that for an ideal contact interface.