The prediction of the remaining life of a bearing plays a vital role in reducing the accident-related maintenance costs of machinery and in improving the reliability of machinery and equipment. To predict bearing remaining useful life (RUL), the abilities of statistical characteristics to reflect the bearing degradation state differ, and the single prediction model has low generalization ability and a poor prediction effect. An ensemble robust prediction method is proposed here to predict bearing RUL based on the construction of a bearing degradation indicator set: the initial bearing degradation indicator subsets were constructed using the Fast Correlation-Based Filter with Approximate Markov Blankets (FCBF-AMB) and Maximal Information Coefficient (MIC) selection methods. Through the cross-operation of the obtained subsets, we obtained a set of robust degradation indicators. These selected degradation indicators were fed into the long short-term memory (LSTM) neural network prediction model enhanced by the AdaBoost algorithm. We found through calculation that the average prediction accuracy of the proposed method is 91.40%, 92.04%, and 93.25% at 2100, 2250, and 2400 rpm, respectively. Compared with other methods, the proposed method improves the prediction accuracy by 1.8% to 14.87% at most. Therefore, the method proposed in this paper is more accurate than the other methods in terms of RUL prediction.