Residual useful life (RUL) prediction is significant for condition-based maintenance. Traditional data-driven RUL prediction method can only predict fault trend of the system rather than RUL of a specific system component. Thus it cannot tell the operator which component should be maintained. The innovation of this paper is as follows: (1) Wavelet filtering based method is developed for early detection of slowly varying fault. (2) Designated component analysis is introduced as a feature extraction tool to define the fault precursor of a specific component. (3) Exponential life prediction model is established by nonlinear fitting of the historical RUL and the fault size characterized by the statistics used. Once online detection statistics is obtained, real-time RUL of the critical component can be predicted online. Simulation shows the effectiveness of this algorithm.