Online discussion has become a main way for people to communicate opinions. Besides posting statements, users are also encouraged to reply to existing posts, revealing support or disapproval of others' viewpoints. Identifying argumentative relations between these interactive texts can benefit modeling the dialogue structure, detecting public opinions, and supporting business, marketing, and government to make decisions. Existing studies detected argumentative relations by constructing overall semantic information or conditional semantic information, but the contextual relevance information between interactive texts was ignored. This work proposed a co-attention contextual relevance network (CCRnet). With the co-attention mechanism, the model captured bi-directional attention between the post and reply. Experimental results on the CreateDebate dataset show that he proposed model outperforms the state-of-the-art models. Furthermore, the visualization of the similarity matrix illustrates the effectiveness of the co-attention mechanism.