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In the framework of the relativistic mean field theory,we investigate (K)0 condensation along with Kˉcondensation occur well in the core of the maximum mass stars for relatively shallow optical potentials of (K) in the range of-100 MeV～-160 MeV.With the increasing optical potential of (K),the critical densities of (K) decrease and the species of baryons appearing in neutron stars become fewer.The main role of (K)0 condensation is to make the abundances of particles become identical leading to isospin saturated symmetric matter including antikaons,state,which leads to a large reduction in the maximum masses of neutron stars.In the core of massive neutron stars,neutron star matter including rich particle species,such as antikaons,nucleons and hyperons,may exist.