Rolling element bearing is one of the critical components in rotating machines, and its running state determines machinery Remaining Useful Life (RUL). Estimating impending failure and predicting RUL of bearing is beneficial to schedule maintenance strategy and avoid abrupt shutdowns. This paper presents a novel method of RUL prediction of bearings, which can evaluate the degradation stage of bearings through dimensionless measurements and exploit the optimal RUL prediction through hybrid degradation tracing model in degradation stage. Two new measurements reflect the vibration intensity of bearings regarding normal vibration value. They can eliminate individual differences of bearings, improve sensitivity to the incipient defect of bearings, and reduce fluctuation. Moreover, they are helpful to detect the time to start prediction and set dimensionless failure threshold. SVM classifier is used to assess the degradation stage of bearing, which shows a high classification accuracy because of its excellent generalization ability and mathematical foundation. As input, the fitted measurements based on the generalized degradation model are used to train the SVM classifier. As output, five degradation stages are defined. However, actual measurements are used as inputs in the prediction process. According to the classification results, a hybrid degradation tracing model is utilized to exploit the optimal RUL prediction by tracking the degradation process of bearings. The proposed method is validated on the public IMS and PRONOSTIA bearing datasets, and its performance is compared with other methods on PRONOSTIA bearing datasets. The results show that the proposed approach is an effective way for RUL prediction of bearings within the prescribed error range. Given that the proposed measurements are dimensionless, this method can be applied under different operating conditions.