In this paper, a novel method combining the localized boundary knot method (LBKM) and a semi-analytical formulation is developed for analyzing SH wave scattering problems in half spaces. To solve the problem effectively, the computational domain is divided into a finite interior domain containing all scatterers and an infinite exterior region by a semicircle. In the finite domain, the LBKM, which is accurate and yields a sparse coefficient matrix, is employed. For the infinite exterior region, the solution is expressed by a semi-analytical formulation that exactly satisfies both the governing equation and the Sommerfeld radiation condition. The two formulations are then coupled through interface conditions. Three numerical examples involving the scattering of SH waves by canyons, underground tunnels, and inclusions were conducted to validate the proposed method. Its superior performance is illustrated through a comparison with the generalized finite difference method, localized method of fundamental solution, and radial point interpolation method. For the cases without analytical solutions, the effectiveness of the proposed approach is validated via the results from the finite element method.