We report on a calculation of BK with domain wall fermion action in quenched QCD. Simulations are made with a renormalization group improved gauge action at β = 2.6 and 2.9 corresponding to a-1 ≈ 2GeV and 3GeV. Effects due to finite fifth dimensional size N5 and finite spatial size Nσ are examined in detail. Matching to the continuum operator is made perturbatively at one loop order. We obtain BK(μ = 2GeV) = 0.5746(61), where the error is statistical only, as an estimate of the continuum value in the scheme with naive dimensional regularization. This value is smaller but consistent with BK(μ = 2GeV) = 0.628(42) obtained by the JLQCD Collaboration using the Kogut-Susskind quark action. Results for strange quark mass are also reported.