Earthquake magnitude prediction is an extremely difficult task that has been studied by various machine learning researchers. However, the redundant features and time series properties hinder the development of prediction models. Elite Genetic Algorithm (EGA) has the advantages in searching optimal feature subsets, meanwhile, Long Short-Term Memory (LSTM) is dedicated to processing time series and complex data. Therefore, we propose an EGA-based feature selection of LSTM model (EGA-LSTM) for time series earthquake prediction. First, the acoustic and electromagnetics data of the AETA system we developed are fused and preprocessed by EGA, aiming to find strong correlation indicators. Second, LSTM is introduced to execute magnitude prediction with the selected features. Specifically, the RMSE of LSTM and the ratio of selected features are chosen as fitness components of EGA. Finally, we test the proposed EGA-LSTM on the AETA data of Sichuan province, including the influence of data in different periods ($timePeriod$) and fitness function weights ($\omega_a$ and $\omega_F$) on the prediction results. Linear Regression (LR), Support Vector Regression (SVR), Adaboost, Random Forest (RF), standard GA (SGA), steadyGA, and three Differential Evolution Algorithms (DEs) are adopted as our baselines. Experimental results demonstrate that all the methods can get the best performance when $timePeriod = 0:00-8:00$, $\omega_a=1$, and $\omega_F=0.8$. Moreover, our proposed approach is superior to state-of-the-art approaches on the evaluation indicators MAE, MSE, RMSE, and $R_2$. Non-parametric tests reveal that EGA-LSTM is significantly different from others and outperforms the standard LSTM.