Accurate remaining useful life (RUL) prediction of critical assets is an important challenge in condition based maintenance to improve reliability and decrease machine's breakdown and maintenance's cost. Bearing is one of the most important components in industries which need to be monitored and the user should predict its RUL. The challenge of this study is to propose an original feature able to evaluate the health state of bearings and to estimate their RUL by Prognostics and Health Management (PHM) techniques. In this paper, the proposed method is based on the data-driven prognostic approach. The combination of Simplified Fuzzy Adaptive Resonance Theory Map (SFAM) neural network and Weibull distribution (WD) is explored. WD is used just in the training phase to fit measurement and to avoid areas of fluctuation in the time domain. SFAM training process is based on fitted measurements at present and previous inspection time points as input. However, the SFAM testing process is based on real measurements at present and previous inspections. Thanks to the fuzzy learning process, SFAM has an important ability and a good performance to learn nonlinear time series. As output, seven classes are defined; healthy bearing and six states for bearing degradation. In order to find the optimal RUL prediction, a smoothing phase is proposed in this paper. Experimental results show that the proposed method can reliably predict the RUL of rolling element bearings (REBs) based on vibration signals. The proposed prediction approach can be applied to prognostic other various mechanical assets.