The friction-induced vibration of a novel slider-on-rotating-disc system is studied by a combination of numerical analysis on the theoretical model and experimental investigation on the test rig. In this system, the rotation of an L-shaped component couples with the friction-induced stick–slip vibration in the tangential direction and produces a state-dependent normal force. The numerical results of the dynamic responses by employing the Coulomb friction model and the friction model with Stribeck effect are both in good agreement with the experimental results, therefore the credibility of the numerical analysis on the theoretical dynamic model is validated. The bi-stability phenomenon, i.e., there is coexistence of a stable pure sliding response and a stable stick–slip limit cycle in a certain parameter range, is not only revealed in the numerical analysis but also observed experimentally. Moreover, a novel approach to constitute a non-uniform friction interface on the disc surface is explored for its efficacy in suppressing the friction-induced stick–slip vibration of the system also by both numerical analysis and experimental testing, namely, the disc surface is divided into sectors assigned with different friction properties. Both the numerical and experimental results show that the non-uniform friction interface of the disc with appropriate friction properties of these sectors can be an effective approach to diminish the range of the operating parameters where the stick–slip vibration occurs and thereby reduce the possibility of occurrence of stick–slip vibration in the system.