You can claim a 15% tax credit on education expenses paid for yourself or a dependent who qualifies for the basic deduction. Your own education expenses — even graduate school — are deductible with no cap. Dependents have per-person caps: KRW 3 million/year for preschoolers through high schoolers, and KRW 9 million/year for university students (graduate school doesn't count as a "dependent" for this purpose, so only the taxpayer's own graduate tuition qualifies).
If your child attends a Korean school (kindergarten through university) as a foreign national, the same credit applies.
What counts as deductible education expenses
Private academy fees are NOT deductible
Private tutoring or cram-school (hagwon) fees for elementary through high-school students do not qualify. An exception exists only for preschoolers' academy fees run on a monthly basis. Tuition at foreign or international schools may qualify if the school is officially recognized — confirm in advance.