The purpose of this study is to examine the mediating effects of positive psychological capital and psychological burnout in the relationship between intrapersonal intelligence and respect for children’s rights among childcare teachers. This study explores the psychological mechanisms of childcare teachers that help to strengthen children’s rights in childcare centers. A survey of childcare teachers was conducted in Gyeonggi-do Province in Korea. Out of 560 copies of the questionnaire that were distributed, 502 were returned, and 465 were used for the analysis after questionnaires with incomplete responses were excluded. The collected data were analyzed using PROCESS macro version 4.0 to examine whether positive psychological capital and psychological burnout mediated the relationship between intrapersonal intelligence and respect for children’s rights. The results of this study showed close relationships among all variables. The mediation analysis showed that positive psychological capital and psychological burnout had sequential mediating effects in the relationship between intrapersonal intelligence and respect for children’s rights. Childcare teachers first must increase their positive psychological capital to protect and respect children’s rights. Also, educational programs tailored for childcare teachers must be developed for better psychological well-being to promote respect for children’s rights in the classroom.