The dipole magnet of the China Spallation Neutron Source (CSNS) Rapid-cycling Synchrotron (RCS) will be operated at a 25 Hz sinusoidal alternating current which causes severe vibration. The vibration will influence the long-term safety and reliable operation of the dipole magnet. By taking the dipole magnet and magnetic measurement girder as specific model system, a method for analyzing and studying the dynamic characteristic of the system is put forward by combining theoretical calculation with experimental testing. This paper established the mechanical model of the system, and the top six step natural frequency and vibration mode were obtained through theoretical modal analysis (ANSYS). Then according to testing modal analysis, the natural frequency, damping ratios and vibration mode of the system structure were obtained too. The theoretical modal analysis results coincide with the experimental testing results. Besides, the 6th step natural frequency is close to the exciting frequency of the magnet, so the resonance phenomenon may take place at the actual working conditions. The dynamic characteristic data of the structure can provide an analysis basis for the further study and the formal dipole magnet girder optimal design of RCS.