In order to consider the attenuation effect of the pore medium on the wave propagation deformation, linear resistance, nonlinear resistance and inertial force are introduced in the governing equations of the permeable medium fluid. The exact kinematic and kinetic boundary conditions are used on free surface, and the exact kinetic boundary conditions are adopted on the underwater boundary conditions, and the vertical velocity satisfies the continuity and the horizontal velocity satisfies the momentum equality condition between the free water and the water in permeable medium. Firstly, the three-dimensional Boussinesq-type water-wave equations expressed in two sets of computational velocities with the highest spatial derivative of 3 were derived to suit the wave motion of single-layer permeable seabed. Secondly, Fourier analysis was performed on the newly-presented equations, and the phase velocities and decay rates of the equations were compared with the analytical solutions of Stokes linear waves. The analytical solutions of the equation are in good agreement with the analytical solutions of Stokes linear waves in the range of a dimensionless water depth of h₁/L< 1.0 (deep water wavelength L=gT²/(2π)) at 1% error with a relative water depth of h₂/h₁=0.1-10, which exceeds the range of applicability with any Boussinesq-type model in history. Further, a numerical model of the two-dimensional flume was developed and the numerical model was solved using a prediction-correction-iterative finite-difference method, and a composite fourth-order Adams-Bashforth-Moulton scheme was chosen for time iteration. Finally, the wave evolution over the permeable terrain was simulated and numerical simulations were carried out. Comparison with the relevant experimental results shows a good agreement.