Forecasting the overnight (close-to-open) return direction of a stock market index has recently attracted great attention. Owing to the strong interactions among stock markets around the globe, one stock market would be inevitably affected by others. In this study, we take global stock market indices as an informative source and propose a deep learning approach combining genetic algorithm to forecast the overnight return direction of a target stock market index. Starting from the multiple-branch input layers representing stock market indices from various regions worldwide, we use multiple convolution units to extract the features from each region. These features are then concatenated and connected with fully connected layers to forecast the daily direction of the overnight return. To optimize the deep neural network, genetic algorithm is used to determine the optimal network architecture and parameters. In the experimental study, we apply the proposed model to forecasting the overnight return directions of nine target indices from Asia, Americas and Europe markets. The experimental results indicate that compared with other competing methods, the proposed model is superior in terms of the accuracy, F-measure and Sharpe ratio.