Phase transitions in neutron stars within modified quark-meson coupling model

K-condensation and quark deconfinement phase transitions in neutron stars are investigated. We use the modified quark-meson coupling model for hadronic phase and the MIT bag model for quark phase. With the equation of state (EOS) solved self-consistently, we discuss the properties of neutron stars. We find that the EOS of pure hadron matter with condensed K-phase should be ruled out by the redshift for star EX00748-676, while EOS containing unpaired quark matter phase with B 114 being about 180 MeV could be consistent with both this observation and the best measured mass of star PSR 1913 + 16. But if the recent inferred massive star among Terzan 5 with M > 1.68M(circle dot) is confirmed, all the present EOSes with condensed phase and deconfined phase would be ruled out.