The analytical solutions for the interaction between dislocations and interfaces are of great importance to materials scientists as well as to mechanics researchers. The interfaces are treated as perfectly bonded in the most of the existing research works, where the traction and displacement vectors are continuous across the interfaces. However, in reality, there are discontinuities of displacements across the interfaces. In the present paper, the interaction between a screw dislocation and an imperfect interface is considered. The imperfect interface is modeled by linear spring and dashpot, i.e. linearly elastic and viscoelastic behaviors are introduced to model the imperfection of the interface. Particularly, we solved the boundary value problem analytically for Kelvin and Maxwell type of interface. In terms of geometrical configurations, we obtained the solutions for two joint half-spaces and a circular inclusion embedded in an infinite matrix. The analytical results show that the force acting on the dislocation depends on the mismatch of materials and the imperfection of the interface and evolves as time elapses.