model by a chain of superconducting qubit circuits. Furthermore, we study the environmental effect on topological quantum states of the Kitaev model. Besides the independent environment surrounding each qubit, we also consider the common environment shared by two nearest neighboring qubits. Such common environment can result in an effective non-Hermitian dissipative coupling between two qubits. Through theoretical analysis and numerical calculations, we show that the common environment can significantly change properties of topological states in contrast to the independent environment. In addition, we also find that dissipative couplings at the edges of the chain can be used to more easily tune the topological properties of the system than those at other positions. Our study may open a new way to explore topological quantum phase transition and various environmental effects on topological physics using superconducting qubit circuits.