A superconducting qubit is a quantum two-level system (TLS) implemented with superconducting wires and Josephson junctions. It can combine with a superconducting coplanar waveguide stripline to form a circuit-based cavity quantum electrodynamic (QED) system, where the stripline plays the role of the cavity resonator. The level spacing of the superconducting qubit is tunable by external magnetic flux  . Cavity QED system is a competitive candidate for implementing quantum logic gates, which are basic elements for building quantum computers. Thus, cavity QED is significant for quantum information processing. However, conventional cavity QED system only considers the bare levels of the superconducting qubit, whose  -type structure forbids the direct transition from the ground level to the second excited level, limiting the possible logical operations to be implemented. We therefore consider the dressed system formed by a superconducting qubit in resonant with the cavity resonator. We find that either  -type structure or  -type exists, which allows the direct transition from the ground level to the second excited level. The tunable level spacings not only lead to the splitting of the dressed level states, but also affect the relaxation rates and dephasing rates of the dressed cavity QED system. For interpreting the reason why two types of the level structures coexist in the dressed system, we introduced the novel concept of quasi-two-level system (qTLS). In the simulation result, at two splitting points f0  0.493787 and f1  0.506213 , the ground level and the first excited level degenerate into one level. Furthermore, conventional stripline resonator only allows a single resonant mode of transverse field, limiting the multi-photon transitions in the nonuniform level spacing of the qubit. Thus, we provide a possibility for a multi-band coupling between the superconducting qubit and a cross-shaped resonator (CSR) which is a kind of multi-mode resonators (MMRs) in the cavity. The cross-shaped multi-mode resonator that is coplanar to superconducting qubits can be utilized as a signal controller. It can store standing electromagnetic fields of different frequencies to be resonant with the qubits. Two scenarios of coplanar CSR with different input-output coupling types are proposed. Considering the tunable range of the superconducting qubit from 5 GHz to IV 10 GHz, we obtain two coupling ranges 4.51 GHz ~ 4.59 GHz and 7.07 GHz ~ 7.35 GHz with an edge coupling type, range of 5.39 GHz ~ 5.54 GHz and 7.21 GHz ~ 7.42 GHz with a L-shape coupling type under the simulation of Ansoft HFSS. In order to implement a better coupling performance, the L-shape type with a relatively large scattering parameter magnitude S11 and S21 is a better choice.