The contact interface of gas turbine rod-fastened rotors is complex, leading to a weakening of the overall structural continuity and enhancement of nonlinear characteristics. The structural form of the rod-fastened rotor can induce some special failures, such as uneven distribution of preload and poor contact between the disc interfaces. Therefore, it is crucial to conduct dynamic studies on gas turbine rod-fastened rotors under complex contact states. In this study, a vibration analysis method of gas turbine rod-fastened rotor discs with multi-scale contact interfaces is established based on elastic-plastic contact theory and high-fidelity finite element method. Experimental validation is conducted on a multi-disc center rod-fastened rotor with Hirth coupling, confirming the accuracy of the method. Subsequently, vibration response analysis considering disc contact characteristics is performed on a real heavy-duty gas turbine center rod-fastened rotor. This research can provide a foundation for the dynamic analysis and design of gas turbine rod-fastened rotors.