Accurate life prediction of lithium-ion batteries is essential for the safety and reliability of smart electronic devices, and data-driven methods are one of the mainstream methods nowadays. However, existing prediction methods suffer from the problems such as lack of practical meaning of features and insufficient interpretability. To address this problem, this article proposes a battery degradation and capacity prediction model based on the Granger causality (GC) test and the long short-term memory network. First, initial health indicators are set from the monitoring data of the battery. Second, the vector autoregressive model and the GC test are used to select causal features that are associated with capacity degradation. Then, the impulse response analysis approach is proposed for the first time to analyze the exact influence of the features on capacity degradation and combine the battery aging mechanism, further clarifying the interpretability of the selected features. Finally, using the causal features as model input, a prediction model based on the long short-term memory network is constructed. The experimental results of the two datasets show that the minimum root mean square error is 0.0093 Ah and 0.9635 mAh with the mean relative errors of 0.25% and 0.13%, which verifies the validity and accuracy of the proposed method.