This study considers the incidence of an acoustic wave through a liquid at its boundary with a double-porosity solid, which is saturated with a viscous fluid. This incident wave refracts to the continuing double-porosity medium as four attenuating waves. Of these four waves, three are longitudinal waves, which induce a flow of pore fluid across the dual-porosity network in the porous aggregate. The amount of this fluid flow is expressed in terms of the dilatations of various constituents in composite porous medium. This wave-induced flow in double-porosity solid is separated into the contributions from each of the three longitudinal waves. For the propagation of harmonic waves, each contribution becomes the function of wave frequency. A numerical example is solved to calculate the contributions of three refracted longitudinal waves to the induced fluid flow in double-porosity ocean bed. Due to the normal incidence of acoustic waves, fluid flow is induced mainly by the fastest longitudinal wave. However, for oblique incidence of acoustic wave, it is the slowest longitudinal wave, which induces much of the fluid flow, particularly near critical incidence. To induce a larger flow of pore fluid, the longitudinal waves prefer the pervious ocean bottom. Effects of incident direction, wave frequency, pore fluid viscosity, permeability, radius of spherical inclusions and sealing of boundary pores are analysed on the wave-induced flow of pore fluid.