The method of fundamental solutions (MFS) and domain decomposition method (DDM) are employed to solve the water-wave diffraction by a thin porous vertical breakwater of semi-infinite extent. Based on the linearized theory of water waves, the problem can be reduced to a boundary value problem with degenerate boundary. In contrast to other mesh dependent numerical method, the MFS is easier and more efficient to handle degenerate boundary value problems. Various incident wave angles and porous parameters are included to validate the power of the proposed numerical scheme. The present results demonstrate the MFS is sufficiently accurate and feasible to be used to predict water-wave diffraction by a thin permeable breakwater by comparing with literature.