We study the effect of strangeness on the core of a neutron star. The equation of state for uniform hadronic matter is calculated using the chiral quark-meson coupling model in relativistic Hatree-Fock approach. The MIT bag model with one-gluon-exchange interaction is adopted for a description of quark matter, and the first-order phase transition from hadrons to quarks is assumed under Gibbs criteria for chemical equilibrium. It is found that the maximum mass of a neutron star with hyperons and quarks can support the 2M ⊙ neutron stars due to the Fock contribution, although the quark production softens the EoS. Furthermore, considering the measurements of the massive neutron stars, the strangeness fraction is estimated to be maximally around 14%, and the lower bound of the critical chemical potential of the quark-hadron phase transition turns out to be around 1.4 GeV.