This study aimed to assess whether there is a bidirectional association between autism spectrum disorder (ASD) and epilepsy in child and adolescent patients. The National Health Insurance Research Database of Taiwan was used to conduct two cohort studies of patients who were under 18 years of age during the period 1997–2008. Cohort 1 comprised patients with newly diagnosed ASD but excluded those diagnosed with epilepsy prior to ASD. A non-ASD comparison group was matched to each case in terms of age and sex. Cohort 2 comprised patients with newly diagnosed epilepsy but excluded those diagnosed with ASD prior to epilepsy. A non-epilepsy comparison group was matched to each case in terms of age and sex. We calculated the incidence of epilepsy in patients with ASD and hazard ratio (HR) to estimate the risk of epilepsy in association with ASD in cohort 1, and the reverse in cohort 2. In cohort 1, the incidence of epilepsy was 13.7 in the ASD group and 1.3 in the non-ASD group (per 1000 person-years). The adjusted HR for epilepsy was 8.4 (95 % CI 5.5–12.7) in the ASD group when compared with the non-ASD group. In cohort 2, the incidence of ASD was 3.4 in the epilepsy group and 0.3 in the non-epilepsy group (per 1000 person-years). The adjusted HR for ASD was 8.4 (95 % CI 6.2–11.4) in the epilepsy group when compared with the non-epilepsy group. A bidirectional association was, therefore, found to exist between ASD and epilepsy. These findings implicate that ASD and epilepsy probably share common risk factors. However, further studies are required to reveal more detail on the mechanism of this bidirectional association.