Prediction of the financial market price is critical for financial decision-making and market policy-making. Recently, various machine learning and deep learning methods have been adopted to predict financial markets’ movements using historical time series of prices. However, accurate prediction of financial prices is still a long-standing challenge that always calls for new approaches. In this study, a novel machine learning model of reservoir computing is developed to predict stock market indices. The performance of the proposed new model is systematically evaluated using the time series of daily closing prices of seven major international stock market indices including S&P500 Index, New York Stock Exchange Composite, Dow Jones Industrial Average, Nasdaq Composite Index, Financial Times Stock Exchange 100 Index, Nikkei 225 Index, and Shanghai Stock Exchange Index between January 4, 2010, and December 31, 2018 covering 2,272 trading days. The results show that our model outperforms the widely used deep learning methods of long short-term memory and recurrent neural network in most cases. To further evaluate the predictive capability of our model, we compare our model to the other two newly reported deep learning methods in recent studies. Comparative results also show that our model is competitive to those deep learning methods in predicting stock market indices. Our study contributes to the literature by developing novel reservoir computing models for financial market predictions. Meanwhile, our results also provide practical implications for financial practitioners of potential financial applications of reservoir computing in financial time series analysis and predictions.