Executive function and intelligence are negatively associated with aggression, yet the role of executive function has rarely been examined in the context of school bullying. We studied whether different domains of executive function and non-verbal intelligence are associated with bullying involvement in early elementary school. The association was examined in a population-based sample of 1,377 children. At age 4 years we assessed problems in inhibition, shifting, emotional control, working memory and planning/organization, using a validated parental questionnaire (the BRIEF-P). Additionally, we determined child non-verbal IQ at age 6 years. Bullying involvement as a bully, victim or a bully-victim in grades 1–2 of elementary school (mean age 7.7 years) was measured using a peer-nomination procedure. Individual bullying scores were based on the ratings by multiple peers (on average 20 classmates). Analyses were adjusted for various child and maternal socio-demographic and psychosocial covariates. Child score for inhibition problems was associated with the risk of being a bully (OR per SD = 1.35, 95%CI: 1.09–1.66), victim (OR per SD = 1.21, 95%CI: 1.00–1.45) and a bully-victim (OR per SD = 1.55, 95%CI: 1.10–2.17). Children with higher non-verbal IQ were less likely to be victims (OR = 0.99, 95%CI: 0.98–1.00) and bully-victims (OR = 95%CI: 0.93–0.98, respectively). In conclusion, our study showed that peer interactions may be to some extent influenced by children’s executive function and non-verbal intelligence. Future studies should examine whether training executive function skills can reduce bullying involvement and improve the quality of peer relationships.