We study the one-dimensional Kitaev-Heisenberg model as a possible realization of magnetic degrees of freedom of the K-intercalated honeycomb-lattice ruthenium trichloride α-RuCl₃, denoted as K_0.5RuCl_m. First, we discuss the possible charge ordering pattern in K_0.5RuCl_m, where half of the j=[Formula presented] spins are replaced by nonmagnetic ions in the honeycomb layer. Next, we investigate the low-energy excitations of the 1D Kitaev-Heisenberg model by calculating the dynamical spin structure factor using the Lanczos exact-diagonalization method. In the vicinity of Kitaev limit, there exist two well-separated dispersions. The bandwidth of each dispersion depends on the Heisenberg and Kitaev terms. This result may be relevant to the low-lying magnetic excitations of K_0.5RuCl_m.