Fault prognosis is an important step to achieve condition-based maintenance for machinery systems. The existing fault prognostic methods can generally be categorized into three major classes: case-based, data-driven, and model-based methods. This paper proposes a novel case-based data-driven prognostic framework based on the adaptive neuro-fuzzy inference system (ANFIS) and big data concept. The framework contains two phases. One is an offline learning phase, in which big historical data are used to build an ANFIS model-case library. The other is the online prognostic phase, in which the fault prognosis of a new machinery system (i.e., a new case) is accomplished by using the proper ANFIS model(s) chosen from the model-case library. The proposed framework is tested by using the experimental data of bearing faults collected from a bearing test rig. Result shows that it has better fault prognostic accuracy than the traditional data-driven method.