In this paper, we present two methods to identify and categorize the offensive language in Twitter. In the first method, we establish a probabilistic model to evaluate the sentence offensiveness level and target level according to different sub-tasks. In the second method, we develop a deep neural network consisting of bidirectional recurrent layers with Gated Recurrent Unit (GRU) cells and fully connected layers. In the comparison of two methods, we find both method has its own advantages and drawbacks while they have similar accuracy.