This paper proposes a series solution for studying the ground motion of twin-peaks hill, double triangular hills, and hill-canyon composite topography. The propagation medium of SH wave is linearly elastic, isotropic, and homogeneous. A flexible multi-region-matching technique (MRMT) and complex function method are adopted to construct the wave field expression in each sub-region. To solve the unknown coefficients in the wave field expressions, Fourier series expansion method in the complex domain is adopted. Finally, some typical numerical examples are calculated to analyse the influence of the topography shape parameters, wave number, and the incident angle on ground motion.