SUMMARY In this study, we present a semi-analytical method to simulate the propagation of seismic waves in horizontally stratified double-porosity media. We solve the governing equations in the frequency–wavenumber domain and then compute the time–space domain solutions by Hankel and fast Fourier transforms. We conduct numerical simulations to study the properties of the seismic waves in the double-porosity media. The results show the existence of three P waves, one fast P wave and two slow P waves. The two slow P waves are highly attenuated and can be observed by assuming a low fluid viscosity. By comparing the fast P wave in a single-porosity medium and that in a double-porosity medium, we find that the double-porosity model predicts much higher attenuation of the fast P wave due to the local fluid flow between the background medium and the inclusions. We also study the parameters affecting the attenuation, such as the radius of the spherical inclusions, the viscosity of the pore fluid, the permeability of the background medium and the porosity of the inclusions. Finally, we present a cross-well survey model to investigate the seismic responses in the double-porosity media and compare them with the responses in the single-porosity media. We find that both the amplitude and velocity of the fast P wave decrease with the increase of the volume ratio of the inclusions.