Anti-Bullying and Harassment Act of 2018 This bill amends the Safe and Drug-Free Schools and Communities Act to require: (1) states to use grants for safe and drug-free schools to collect and report information on the incidence of bullying and harassment, and (2) local educational agencies (LEAs) and schools to use subgrants to prevent and respond to incidents of bullying and harassment. Such LEAs and schools must: (1) notify parents and students annually of conduct prohibited in their school discipline policies, which must include policies regarding bullying and harassment; and (2) establish complaint procedures for students and parents to register complaints regarding such conduct. The bill also expands the Act's definition of violence to include bullying and harassment.