In this thesis, we calculate the kaon B-parameter BK in quenched lattice QCD with exact chiral symmetry. Our computations are performed at lattice spacing about 0.147(1) fm with gauge configurations generted by Wilson gauge action at β = 5.8 on a 83 × 24 lattice. Our bare BK is renormalized non-perturbatively in the Landau gauge. Our preliminary results are BRI K (1.88GeV ) = 0.6561± 0.2636 at mq = 81.63 MeV and BRI K (1.88GeV ) = 0.8146 ± 0.2468 at mq = 108.84 MeV.