Cyberbullying is a social problem in the digital age. Online social networks have been reported to be linked with cyberbullying, but the links remain unclear. Our research question is “Do social norms that allow cyberbullying spread via online social networks?” The objectives of our study are to answer this research question and clarify the effects of online social networks on cyberbullying from the perspective of a complex contagion model. Participants were 129,164 users in Pigg Party, which is a Japanese online chat platform with avatar. Their status of cyberbullying perpetrators and victims was estimated using a combination of questionnaire and machine learning methods. Results showed that both cyberbullying perpetrator and victim rates among their peers and among the peers of their peers increased participants' risk of becoming cyberbullying perpetrators. Similarly, these rates increased their risk of becoming cyberbullying victims. As their intimacy with cyberbullying perpetrators increased, their risks of perpetrating cyberbullying increased. However, as their intimacy with the perpetrators increased, their risks of becoming cyberbullying victims decreased. The social contagion of cyberbullying via online peer networks and the perpetrator's rational choice of cyberbullying victims are discussed.