This research is for the purpose of understanding the relationships between core competencies and co-opetition of concatenate children?s English supplementary education institutions in Taichung city. The author has interviewed five concatenate children?s English supplementary education institutions for understanding the status of concatenate children?s English supplementary education market as the authority of the questionnaire. After designing the questionnaire, five authorities in this field were invited to offer their suggestions for improvement of the questionnaire. Then actualize prelim to make sure the reliability and availability. The formal questionnaire has three parts, including?the core competencies of concatenate children?s English supplementary education institutions?,?the co-opetition of concatenate children?s English supplementary education institutions?and?the background of concatenate children?s English supplementary education institutions ?, adopting the investigation of questionnaire to all 105 concatenate children?s English supplementary education institutions in Taichung city. The collected data was analyzed using factor analysis and cluster analysis to generalize the types of core competencies and co-opetition. Using Chi-squared test to analyze if core competencies and co-opetition has significantly different in defferent background of concatenate children?s English supplementary education institutions. To verify those hypotheses in the research and understand the relationships between core competencies and co-opetition. The conclusion and suggestions will be offered to concatenate children?s English supplementary education institutions for further research.