This study examined the mechanism of peer network(status, similarity, reciprocity) character(overt, covert), bullying(exclusion, mocking) in the elementary school. Recently several teachers and parents have argued that some students don\'t make a friend with peers. And they have been excluded in their class activity. Of course excluding students have a few problems of personality. And the bullying was connected with the peer network and the character. Developed the new SEM about peer network, character, bullying and was tested by LISREL. For this study was used three test tools, which are Peer network, character, bullying. Surveyed 12 elementary schools and 737 children. The reliability of three questionnaires was .93, .92, .84(Cronbach alpha). Results are as follows. First, founded that children choose their friends according to the reciprocity. But peer network was few associated with character. Second, through model testing it appeared that this model is very good. The chi-square with 10 degrees of freedom was 17.71(p>.05). The goodness-of-fit indices was .99. These statistics indicated that the triangle model fits the data. In conclusion, these results show that we must help students make friends in order to prevent the excluding of peers. Implications of these findings for the preventing of peer bullying were discussed.