We constructed a hypothetical model of the knowledge of autism spectrum disorder (ASD) and self-perception of support of staff working in after-school day services to clarify structural relationships. A questionnaire survey was conducted at 194 facilities providing after-school day services in Fukushima Prefecture (October 2020), including a basic attributes questionnaire, the Literacy Scale of Characteristics of Autistic Spectrum Disorder (LS-ASD), and a staff questionnaire. We developed a hypothetical model of the relationship between self-perception and LS-ASD total scores of after-school service staff. To obtain latent variables for structural equation modeling (SEM) to confirm factor extraction and the interrelationships among variables, exploratory factor analysis was performed. SEM was used to examine the fit of the hypothetical model to the data and the relationships among variables. The study included 302 staff members from 58 of 194 facilities. Four factors (Factor 1, motivation; 2, self-perception of knowledge; 3, information sharing; 4, self-confidence) were extracted. The final model showed that Factor 2 had a positive direct effect (path coefficient = 0.64) and Factor 4 had a negative direct effect (path coefficient = -0.22) on LS-ASD scores. The model goodness of fit was acceptable (Goodness-of-Fit Index = 0.890; Comparative Fit Index = 0.912; Root Mean Square Error of Approximation = 0.086; Akaike's Information Criterion = 392.7). Self-perception of knowledge contributes greatly to knowledge acquisition, while excessive confidence may hinder knowledge retention.