As an essential part of risk investment and a microcosm of the national economy, predicting the stock market's change accurately and efficiently becomes extremely important. The purpose of this paper is to evaluate the accuracy of SVM and LSTM models to judge whether the Efficient Markets Hypothesis (EMH) is correct or not by predicting the typical stock indexes of the relatively mature American stock market and the gradually mature Chinese stock market. Therefore, this article applies the Kaggle Data Set to predict the stock price of S&P 500 and SSEC from January 01, 2013 to January 01, 2018 by using both the LSTM model and the SVM model. First, this paper compares the predicted trends with the actual trend respectively. Second, this paper compares the two stocks and concludes the efficiency of markets in different countries. Third, this paper analyzes the influence of different policies on stock market fluctuation to explain the unpredictable change in the stock market. Finally, according to the results, the statistically significant conclusions are drawn that LSTM is more stable and accurate than SVM in the stock indexes prediction and American stock market is more effective than the Chinese stock market. Therefore, relevant forecasters can be more inclined to use LSTM model when making predictions.