With the rapid growth of the new energy vehicle industry, it is increasingly crucial to monitor and predict the health of lithium batteries. In the field of new energy vehicles, lithium batteries play a significant role, and monitoring their state of health (SOH) is crucial. This study proposes an enhanced algorithm, AM-LSTM, based on Long Short-Term Memory network (LSTM) combined with attention mechanism to improve SOH prediction accuracy. Experiments on NASA-provided datasets show that the AM-LSTM neural network significantly improves prediction accuracy compared to traditional LSTM and GRU networks. For SOH evaluation of lithium batteries B0005, B0006, B0007, and B0018, we observed improvements in accuracy by 15.1%, 21.7%, 14.0%, and 16.0% respectively. This paper summarizes current research on SOH prediction for lithium batteries while also identifying future research directions such as considering additional environmental factors and validating models using different types of battery data to enhance universality and accuracy. However, it is worth noting that our current study only made predictions for two sets of lithium battery data from one model without considering environmental factors like temperature which limits the universality and broad application potential of our findings. Future research will expand into more application scenarios including SOH prediction for lithium batteries in various environments, different models, capacities as well as verification through real vehicle data to achieve comprehensive and accurate monitoring and evaluation of lithium battery health status.