In the framework of superconducting hybrid systems, we construct a star quantum network in which a superconducting transmission line resonator as a quantum bus and multiple units constituted by transmission line resonator and superconducting qubits as the carriers of quantum information. We further propose and analyze a theoretical scheme to realize quantum information processing in the quantum network. The coupling between the bus and any two superconducting qubits can be selectively implemented based on the dark state resonances of the highly dissipative transmission line resonators, and it can be found that quantum information processing between any two units can be completed in one step. As examples, the transmission of unknown quantum states and the preparation of quantum entanglement in this quantum network are investigated. At last, we exhibit our simulation results and complete the relevant discussions in order to show the advantages of this kind of quantum network.