•A general solution is presented for RUL prediction of nonlinear deterioration process.•KPCA is selected for dimensionality reduction and nonlinear feature extraction.•GRU is presented to replace LSTM, which behaves better both in prediction accuracy and training time. Remaining useful life (RUL) prediction is a key process for prognostics and health management (PHM). However, conventional model-based methods and data-driven methods for RUL prediction are bad at a very complex system with multiple components, multiple states and therefore extremely large amount of parameters. In order to solve the problem, a general two-step solution is proposed in this paper. In the first step, kernel principle component analysis (KPCA) is applied for nonlinear feature extraction. Then, a novel recurrent neural network called gated recurrent unit (GRU) is presented as the second step to predict RUL. GRU network is capable of describing a very complex system because of its specially designed structure. The effectiveness of the proposed solution for RUL prediction of a nonlinear degradation process is proved by a case study of commercial modular aero-propulsion system simulation data (C-MAPSS-Data) from NASA. Results also show that the proposed method requires less training time and has better prediction accuracy than other data-driven methods.