We extend the quark mean-field ( QMF ) model to strangeness freedom to study the properties of hyperons ( \Lambda, \Sigma, \Xi ) in infinite baryon matter and neutron star properties . The baryon-scalar meson couplings in the QMF model are determined self-consistently from the quark level , where the quark confinement is taken into account in terms of a scalar-vector harmonic oscillator potential . The strength of such confinement potential for u,d quarks is constrained by the properties of finite nuclei , while the one for s quark is limited by the properties of nuclei with a \Lambda hyperon . These two strengths are not same , which represents the SU ( 3 ) symmetry breaking effectively in the QMF model . Also , we use an enhanced \Sigma coupling with the vector meson , and both \Sigma and \Xi hyperon potentials can be properly described in the model . The effects of the SU ( 3 ) symmetry breaking on the neutron star structures are then studied . We find that the SU ( 3 ) breaking shifts earlier the hyperon onset density and makes hyperons more abundant in the star , in comparisons with the results of the SU ( 3 ) symmetry case . However , it does not affect much the star ’ s maximum mass . The maximum masses are found to be 1.62 ~ { } M _ { \odot } with hyperons and 1.88 ~ { } M _ { \odot } without hyperons . The present neutron star model is shown to have limitations on explaining the recently measured heavy pulsar .