In this paper, we propose a novel model for time series prediction in which difference-attention LSTM model and error-correction LSTM model are respectively employed and combined in a cascade way. While difference-attention LSTM model introduces a difference feature to perform attention in traditional LSTM to focus on the obvious changes in time series. Error-correction LSTM model refines the prediction error of difference-attention LSTM model to further improve the prediction accuracy. Finally, we design a training strategy to jointly train the both models simultaneously. With additional difference features and new principle learning framework, our model can improve the prediction accuracy in time series. Experiments on various time series are conducted to demonstrate the effectiveness of our method.