The paper deals with propagation of SH waves in a viscoelastic layer over a couple stress substrate with imperfect bonding at the interface. A dispersion equation of SH waves in a viscoelastic layer overlying the couple stress substrate with an imperfect interface between them has been obtained. Dispersion equations for propagation of SH waves with perfectly bonded interface and slippage interface between two media are also obtained as particular cases. Effects of the degree of imperfectness of the interface are studied on the phase velo- city of SH waves. The dispersion curves are plotted and the effects of material properties of both couple stress substrate and viscoelastic layer are studied. The effects of internal micro- structures of the couple stress substrate in terms of characteristic length of the material are presented. The effects of heterogeneity, friction parameter and thickness of the viscoelastic layer are also studied on the propagation of SH waves.