Blade tip timing technology is a non-contact measurement technology that is popular in recent years and can be used for the health monitoring of the entire stage, which provides the possibility for online monitoring and fault diagnosis of rotor blade vibration. Aiming at the common rubbing faults of rotor blades, the single-blade and whole-stage dynamic models were established respectively, and the dynamic responses of the blade tips under the rubbing faults of the above two models were analyzed. The characteristics of the blade tip timing signals of sensors and blades in the state of rubbing were expounded, and the feature extraction of the undersampling signal of the blade tip timing was carried out by the enhanced sparse decomposition algorithm. A set of procedures for diagnosing rubbing faults was proposed. The effectiveness of the proposed method is verified by a self-built rubbing test bench.