In this paper, a novel method is developed for day-ahead daily river-flow forecasting based on convolutional neural network (CNN). The proposed method incorporates both spatial and temporal information to improve the forecasting performance. A CNN model is usually trained by minimizing the mean squared error which is, however, sensitive to few particularly large errors. This character of squared error loss function will result in a poor estimator. To tackle the problem, a robust loss function is proposed to train the CNN. To facilitate the training of CNNs for multiple sites forecasting, transfer learning is also applied in this study. With transfer learning, a new CNN inherits the structure and partial learnable parameters from a well-trained CNN to reduce the training complexity. The forecasting performance of the proposed method is validated with real data of four rivers by comparing with widely used benchmarking models including the autoregressive model, multilayer perception network, kernel ridge regression, radial basis function neural network, and generic CNN. Numerical results show that the proposed method performs best in terms of the root mean squared error, mean absolute error, and mean absolute percentage error. The two-sample Kolmogorov-Smirnov test is further applied to assess the confidence on the conclusion.