The scaled boundary finite-element method (SBFEM) by Tao et al. (Comput. Methods Appl. Mech. Engrg 2007; 197:232-242) is only applicable for wave scattering problems by a structure of homogenous material. In this paper, the SBFEM is extended to deal with the interaction of water waves and porous offshore structure with a partially solid wall or opening. The cylindrical structure is considered as a circular cylinder of anisotropic material in the form of variable porosity. A central feature of the newly extended method is that the non-homogenous term caused by the complex configuration of the structure is processed by introducing a variable porous-effect parameter G. This leads to the final scaled boundary finite-element equation is still homogenous and can be solved in a similar manner. The modified SBFEM thus remains a semi-analytical fundamental-solution-less method. Numerical experiments in water wave interaction with a typical coastal/offshore structure-a cylinder with a partially solid wall or opening attest to the efficacy and accuracy of the proposed approach.