Abstract: As one of the most fundamental components in mechanical equipment, rolling bearings shows vibration signals characterized by nonlinearity and non-stationarity. In response to these characteristics, a predictive method for the remaining life of rolling bearings is proposed by integrating variational mode decomposition (VMD) and grasshopper optimization algorithm (GOA) with long short-term memory (LSTM) networks. Firstly, the raw vibration signals including noise are decomposed by VMD. After removing the noise, the decomposition term is reconstructed. Secondly, the time domain features of the denoised signal are extracted. The extracted features are constructed into a continuous time series as the input feature values, and the degradation index is established. The parameters of LSTM model are optimized using GOA method. A predictive model based on GOA-LSTM is proposed. Finally, the validity of the method is verified by the XJTU-SY rolling bearing accelerated life test dataset. The results show that VMD-GOA-LSTM model has higher prediction accuracy and better generalization ability compared with LSTM and VMD-LSTM models. This model can better predict the residual life of rolling bearings.