We study the properties of neutron stars using the chiral quark–meson coupling model, in which the quark–quark hyperfine interaction due to the exchanges of gluon and pion based on chiral symmetry is considered. We also examine the effects of hyperons and Δ-isobars in a neutron star. Extending the SU(6) spin-flavor symmetry to more general SU(3) flavor symmetry in the vector–meson couplings to baryons, the maximum mass of neutron star can reach the recently observed massive pulsar mass, $${1.97 \pm 0.04 M_{\odot}}$$ . In this calculation, Λ and Ξ are generated in a neutron star, while Σ and Δ-isobars do not appear.