We explore the influence of the artificial atomic chain on the input-output relation of the cavity. Specifically, we extend the atom chain to the one-dimensional Su-Schrieffer-Heeger (SSH) chain to check the role of atomic topological non-trivial edge state on the transmission characteristics of the cavity. The superconducting circuits can realize the artificial atomic chain. Our results show that the atom chain is not equivalent to atom gas, and the transmission properties of the cavity containing the atom chain are entirely different from that of the cavity containing atom gas. When the atom chain is arranged in the form of topological non-trivial SSH model, the atom chain can be equivalent to the three-level atom, in which the edge state contributes to the second level and is resonant with the cavity, while the high-energy bulk state contributes to form the third level and is greatly detuned with the cavity. Therefore, the transmission spectrum shows no more than three peaks. This allows us to infer the topological phase of the atomic chain and the coupling strength between the atom and the cavity only from the profile of the transmission spectrum. Our work is helping to understand the role of topology in quantum optics.