There are TWO international school in Kobe offering K12 education.
If you want to explore more schools, you can check out International schools in Osaka. There are many people working in Kobe and living in Osaka for the sake of school and other reasons like proximity to their community. And Vice versa.
Click the below school name(s) to get the details of the international school.
CANADIAN ACADEMY
Higashinada-ku, Kobe, Hyogo-pref.
MARIST BROTHERS INTERNATIONAL SCHOOL
Suma-ku, Kobe, Hyogo-pref.
The below school offers international education until Grade 6.
St. Michael's International School Kobe Japan
Chuo-ku, Kobe, Hyogo-pref