:State-of-health (SOH) is an important indicator for the maintenance and safe operation of batteries, and it is crucial for accurately predicting SOH. To address problems that the noise present in the original data lead to inaccurate prediction results. An Long-Short-Term-Memory (LSTM) method for SOH prediction is proposed based on the joint noise reduction model of complete ensemble empirical mode decomposition adaptive noise (CEEDMAN) and Savitzky-Golay (SG) filtering. Firstly, seven health indicators (HIs) were extracted by analyzing the voltage and current curves, and HIs with higher correlation with SOH were selected using Pearson correlation coefficient. Then, Intrinsic Mode Functions (IMF) components generated from SOH by CEEMDAN are divided into noise-component, noise-dominant-component, useful-signal-dominant-component, filtered noise-dominant-component and useful-signal-dominant-component are reconstructed into filtered SOH. Finally, the LSTM model is used for SOH prediction. Experiments show that proposed model captures the capacity regeneration phenomenon well with high prediction accuracy, and errors are all below 1.9%.