The scaled boundary finite-element method (SBFEM) is a novel semi-analytical approach, with the combined advantages of both finite-element and boundary-element methods. The basic idea behind SBFEM is to discretize the surface boundary by FEM and transform the governing partial differential equations to ordinary differential equations of the radial parameter. The radial differential equation is then solved analytically. It has the inherent advantage for solving problems in unbounded medium with discretization to the interface only. In this paper, SBFEM is applied to solve the wave diffraction by a circular cylinder. The final radial matrix differential equation is solved fully analytically without adoption of any numerical scheme. Comparisons to the previous analytical solutions demonstrate the excellent computation accuracy and efficiency of the present SBFEM approach. It also revealed the great potential of the SBFEM to solve more complex wave-structure interaction problems.