The present study is concerned with the analytical solution for waves propagating over a local permeable seabed and wave reflection and transmission by the local permeable seabed. The computational domain is decomposed into four subdomains of which the middle subdomain is permeable, with the porous seabed beneath it, and the left and right subdomains are impermeable. Applying the linear wave theory, the velocity potential of each fluid subdomain is set up, including the effect of evanescent mode, and the pressure inside the porous seabed is given. The unknowns are solved by the continuous conditions at the interfaces between the neighboring subdomains. The effect of permeability coefficient, water depth and length of permeable seabed on wave transformation is discussed. The results indicate the wave height attenuates increasingly with the increase of permeability coefficient, the length of permeable seabed, and decrease of water depth. Wave reflection and transmission will occur due to the local permeable seabed. The reflection coefficient oscillates, and tends to be constant eventually, while the transmission coefficient reduces exponentially, and tends to be zero with the increase in the length of permeable seabed.