•The EMD-based drift increment extraction method is proposed.•The drift increment is predicted based on the LSTM network.•A difference approximation method for the drift function derivative is proposed.•The drift-increment-based representation of RUL’s PDF is derived.•Advantages in the improvement of the prediction accuracy are justified. In this paper, a novel remaining useful lifetime (RUL) prediction method that fuses stochastic degradation modeling and machine learning is proposed to improve the fitness of the model and quantify the uncertainty of the prediction results. First, a stochastic degradation model based on the Wiener process is built, and the drift increment is extracted using empirical mode decomposition (EMD). Second, a long short-term memory (LSTM) network is trained to learn the equipment degradation rule and predict the drift increment. The diffusion coefficient of the degradation model is then estimated according to the maximum likelihood principle. The final step is to derive the analytical expression for the probability distribution of remaining useful lifetime (RUL) based on the concept of first hitting time and the difference principle. The lithium battery degradation test confirmed the efficacy of the proposed method, achieving a life cycle average prediction accuracy of up to 97.45%.