Nowadays there are large volumes of data in real-world applications, which poses great challenge to class-imbalance learning: the large amount of the majority class examples and severe class-imbalance. Previous studies on class-imbalance learning mainly focused on relatively small or moderate class-imbalance. In this paper we conduct an empirical study to explore the difference between learning with small or moderate class-imbalance and learning with severe class-imbalance. The experimental results show that: (1) Traditional methods cannot handle severe class-imbalance effectively. (2) AUC, G-mean and F-measure can be very inconsistent for severe class-imbalance, which seldom appears when class-imbalance is moderate. And G-mean is not appropriate for severe class-imbalance learning because it is not sensitive to the change of imbalance ratio. (3) When AUC and G-mean are evaluation metrics, EasyEnsemble is the best method, followed by BalanceCascade and under-sampling. (4) A little under-full balance is better for under-sampling to handle severe class-imbalance. And it is important to handle false positives when design methods for severe class-imbalance.