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Recently, more and more data have been generated in the online world, filled with offensive language such as threats, swear words or straightforward insults. It is disgraceful for a progressive society, and then the question arises on how language resources and technologies can cope with this challenge. However, previous work only analyzes the problem as a whole but fails to detect particular types of offensive content in a more fine-grained way, mainly because of the lack of annotated data. In this work, we present a densely annotated data-set COLA (Categorizing Offensive LAnguage), consists of fine-grained insulting language, antisocial language and illegal language. We study different strategies for automatically identifying offensive language on COLA data. Further, we design a capsule system with hierarchical attention to aggregate and fully utilize information, which obtains a state-of-the-art result. Results from experiments prove that our hierarchical attention capsule network (HACN) performs significantly better than existing methods in offensive classification with the precision of 94.37% and recall of 95.28%. We also explain what our model has learned with an explanation tool called Integrated Gradients. Meanwhile, our system's processing speed can handle each sentence in 10msec, suggesting the potential for efficient deployment in real situations.