The kaon B parameter is calculated in quenched lattice QCD with the Wilson quark action. The mixing problem of the Delta s = 2 four-quark operators is solved nonperturbatively with full use of chiral Ward identities, and this method enables us to construct the weak four-quark operators exhibiting good chiral behavior. We find B-K(NDR,2 GeV) = 0.69(7) (where NDR denotes naive dimensional regularization) at the lattice cutoff scale of a(-1) = 2.7-4.3 GeV.