Estimating the remaining useful life (RUL) of equipment is critical for ensuring the safe operation of machinery and reducing maintenance losses. For the existing RUL prediction, the problem of data redundancy and initial prediction time dramatically affects the prediction results. Therefore, this paper proposes a long short-term memory network (LSTM) RUL prediction algorithm that is based on multi-layer grid search (MLGS) optimization. This method integrates feature data and optimizes network parameters to ensure accuracy and effectively predict the non-stationary degradation of the bearing. Firstly, this paper uses a data fusion method to extract low dimensional feature vectors of running data, and the multi-feature fusion is performed to obtain the principal component index. Then, the MLGS is used to optimize the network overparameters. The effect of the initial measurement time on prediction results can be reduced, and the calculation speed can be improved. Finally, the IMS data set of NASA is used for verification and comparative testing. The test results show that the proposed RUL prediction algorithm can effectively reduce the influence of the initial prediction time on the prediction accuracy compared with other prediction methods.