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≈2 and 3 GeV. 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=2 GeV)=0.5746(61)(191), where the first error is statistical and the second error represents an estimate of scaling violation and O(α2) errors in the renormalization factor added in quadrature, as an estimate of the continuum value in the modified minimal subtraction (MS̅) scheme with naive dimensional regularization. This value is consistent, albeit somewhat small, with BK(μ=2 GeV)=0.628(42) obtained by the JLQCD Collaboration using the Kogut-Susskind quark action. Results for light quark masses are also reported.