A time-dependent wave equation is developed for waves propagating over permeable rippled beds taking account of the effects of porous medium. The mean water depth and the thickness of porous layer are assumed to be slowly varying compared to the wavelength of surface waves, and the spatial scale of ripples is assumed to be the same as the wavelength of surface waves. Coupled parabolic equations are formulated from the derived wave equation, following Kirby"s (1986) method. Some numerical examples and experimental results of effects of seabed permeability on the Bragg scattering are shown in one-dimensional case and numerical examples are also shown in two-dimensional case. In the one-dimensional case, we can utilize the Bragg reflection to reduce transmitted waves behind ripples; however, in the two-dimensional case, wave heights behind ripples do not always decrease due to the diffraction effect dependent on the scale of ripple field.