In this paper, we propose on-chip terahertz domino waveguide array structures which can enable the topological effect and enhance the robustness of terahertz transmission. Terahertz topological effect (include topologically-protected edge states and binding states) is excited by constructing kink and antikink structures in designed domino waveguide arrays. Furthermore, the robustness of topological waveguide arrays is successfully demonstrated. The topological transmission effects have been experimentally demonstrated using scanning near-field terahertz microscopy. Our study provides a new approach to study the topological photonic transport of waveguide arrays in the terahertz regime and has potential application in terahertz integrated circuit.