Abstract Based on the control equations for double-porosity media extended from Biot's theory, the propagation of Love waves is discussed in this paper. Dispersion equations of Love waves in double porosity medium are obtained by utilizing the usual assumption of Love waves in elastic solid with the coupling mass coefficient ρ 23 and coupling permeability term k (12) being equal to zero. The dispersion and attenuation properties of Love waves in double porosity medium are analyzed. The approximate limit of the Love wave speed is also given. The effects of fracture porosity and fracture permeability on the behavior of the propagation of Love waves are investigated in detail.