The stator current in an induction motor contains a large amount of information, which is unrelated to bearing faults. This information is considered as the noise component for the detection of bearing faults. When there is noise information in the current signal, it can affect the detection of motor bearing faults and lead to the possibility of false alarms. Therefore, to accomplish an effective bearing fault detection, all or some of these noise components must be properly eliminated. This paper proposes the use of fractional linear prediction (FLP) as a noise elimination method in bearing fault diagnosis, which makes these noise components the predictable components and this bearing fault information the unpredictable components. The basis of the FLP is to eliminate noise components in the current signal by predicting predictable components through linear prediction theory and optimal prediction order. Meanwhile, this paper adopts the FLP model with limited memory samples. After determining the optimal number of memories, only the fractional derivative order parameter needs to be optimized, which greatly reduces the computational complexity and difficulty in parameter optimization. In addition, this paper uses spectral analysis of the current signals through experimental simulation to compare the FLP method with the linear prediction (LP) method and the time-shifting (TS) method that have been successfully applied to bearing fault diagnosis. Based on the analysis results, the FLP method can better extract fault features and achieve better bearing fault diagnosis results, verifying the effectiveness and superiority of the FLP method in the field of bearing fault diagnosis. Additionally, the predictive performance of thevFLP and LP was compared based on experimental data, verifying the advantages of the FLP method in predictive performance, indicating that this method has a better noise cancellation effect.