The remaining useful life (RUL) prediction of rolling bearings has recently gained increasing interest. Many models have been established to catch the degradation performance of bearings. However, there are two shortcomings existing in those models: (1) the health indicator (HI) that used for the first predicting time (FPT) selection is insensitive to incipient faults; (2) the parameter estimation must be based on the historical data, which are not available for some applications due to expensive experiment cost. To overcome the first shortcoming, this paper firstly adopts the mean absolute value of extremums (MAVE) of signals to feature signal energy. Then, the root mean square of the MAVE values (RMS-MAVE) is developed as a new HI to embody signal changes. After that, based on RMS-MAVE values, an adaptive FPT selection approach is proposed by the 3σ approach. For the second shortcoming, through coupling acquired measurement data with the exponential model, a dynamic exponential regression (DER) model based on RMS-MAVE values is proposed to predict the RUL of bearings. The comparison study indicates that RMS-MAVE is superior to the existed ones in FPT selection for distinguishing different health state of bearings, and the DER model performs better than the existed ones in RUL prediction. INDEX TERMS Remaining useful life, rolling bearings, first predicting time, root mean square, the mean absolute value of extremums, dynamic exponential regression model.