Forecasting time series in imbalanced data presents a significant research challenge that requires considerable attention. Although there are specialized techniques available to tackle imbalanced time series prediction, existing approaches tend to prioritize extreme predictions at the expense of compromising the forecasting accuracy of normal samples. We in this paper propose an extreme penalized loss function that relaxes the constraint on overestimating extreme events, thereby imposing great penalties on both normal and underestimating extreme events. In addition, we provide a self-adaptive way for setting the hyperparameters of the loss function. Then, both the proposed loss function and an attention module are integrated with LSTM networks in a decomposition-based framework. Extensive experiments conducted on real-world datasets demonstrate the superiority of our framework compared to other state-of-the-art approaches for both time series prediction and block maxima prediction tasks.